This video is regarding Mathematics Exercise 1.2 of Class 9th Science Group. For further Detail, please visit the followings:-
https://web.facebook.com/brightfuture9703 (Facebook Page)
https://www.youtube.com/@BrightFutureMBS (YouTube Channel)
https://opportunityhubofbrightfuture.blogspot.com/ (Blog)
https://www.dailymotion.com/brightfuture786 (DailyMotion)_
https://www.youtube.com/@ReadandEarnwithMPS (Muhammad Public School & Tuition Academy)
https://web.facebook.com/brightfuture9703 (Facebook Page)
https://www.youtube.com/@BrightFutureMBS (YouTube Channel)
https://opportunityhubofbrightfuture.blogspot.com/ (Blog)
https://www.dailymotion.com/brightfuture786 (DailyMotion)_
https://www.youtube.com/@ReadandEarnwithMPS (Muhammad Public School & Tuition Academy)
Category
📚
LearningTranscript
00:00:00Assalam-o-Alaikum. How are you all? I hope all of you are doing good.
00:00:03Today we will solve exercise 1.2.
00:00:06You can see a wallpaper on the screen which has the timing of all the questions.
00:00:11But I would prefer that you use the time code in the description of this video to reach your required questions.
00:00:17Let's go back to the exercise.
00:00:20You can see question number 1 on the screen.
00:00:22Let's read what is being said in it.
00:00:24From the following matrices, you have to identify.
00:00:37Identify means to identify.
00:00:40Which matrix is the unit matrix?
00:00:43Which matrix is the row matrix?
00:00:46Which matrix is the column matrix?
00:00:47Which matrix is the null matrix?
00:00:49You must have understood this question.
00:00:51In simple words, you have to tell what are the names of these matrices?
00:00:55Which one is null? Which one is row? Which one is column?
00:00:59You will not know this until you know what is unit matrix?
00:01:04What is null matrix?
00:01:05What is column matrix?
00:01:07What is row matrix?
00:01:09The next question in the exercise is also about the identification of matrices.
00:01:13Let's read all the types of matrices in the beginning of this exercise.
00:01:21After that, we will solve the questions one by one and you will understand easily.
00:01:28Let's understand the types of matrices.
00:01:31I have written the topic of types of matrices in the description of this video.
00:01:35The first matrix is row matrix.
00:01:38The name of this matrix is row matrix.
00:01:41If you have learned this in the previous exercise, then you can easily understand this matrix.
00:01:48Row means to write the digits in a horizontal way.
00:01:55In any matrix, there can be one row or more than one row.
00:01:59But in such a matrix, there will be only one row, it will be called row matrix.
00:02:05For example, there is G matrix and M matrix.
00:02:09If I write G, it will be G matrix.
00:02:12How many rows are there in G matrix?
00:02:152, minus 1 and 7.
00:02:17If I highlight G matrix, there is only one row.
00:02:21Therefore, it can be called row matrix.
00:02:24If I talk about M matrix, there is only one row in M matrix.
00:02:271, minus 1.
00:02:29In such a matrix, there is only one row.
00:02:32It is called row matrix.
00:02:35Let's read the definition.
00:02:38A matrix is called a row matrix.
00:02:40A matrix is called a row matrix if it has only one row.
00:02:45If there is only one row in it, like G and M.
00:02:50It was easy to understand.
00:02:53In the previous exercise, we learned about column.
00:02:58Row matrix is also called column matrix.
00:03:01Columns are called columns in a vertical way.
00:03:12Let's read the definition.
00:03:14A matrix is called a column matrix.
00:03:17A matrix is called a column matrix if it has only one column.
00:03:24For example, there was only one row in row matrix.
00:03:26In row matrix, there is only one column in M matrix.
00:03:31In M matrix, there is only one column in N matrix.
00:03:34In such a matrix, there is only one column.
00:03:37It is called column matrix.
00:03:39I hope you have practiced row and column in the previous exercise.
00:03:45Let's read the next matrix.
00:03:48It is called rectangular matrix.
00:03:50A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns.
00:04:13I hope you have understood.
00:04:16A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns.
00:04:25A matrix in which the number of rows is not equal to the number of columns is called a rectangular matrix.
00:04:37Let's read the example.
00:04:42A matrix in which the number of rows is 1, 2, 3.
00:04:48The number of rows is 3.
00:04:51The number of columns is 1 and the number of columns is 2.
00:04:59A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns.
00:05:08Let's read the example.
00:05:10A rectangular matrix is a matrix in which the number of rows is 1, 2, 3.
00:05:20The number of rows is 1 and the number of columns is 3.
00:05:27A rectangular matrix is a matrix in which the number of rows is 1 and the number of columns is 3.
00:05:39The number of rows is 1 and the number of columns is 3.
00:05:50The number of rows is 1 and the number of columns is 3.
00:05:58The number of rows is 1 and the number of columns is 3.
00:06:08A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns.
00:06:15I hope you have understood.
00:06:18Let's read the next example.
00:06:20A square matrix is a matrix in which the number of rows is equal to the number of columns.
00:06:46A square matrix is a matrix in which the number of rows is equal to the number of columns.
00:07:07A square matrix is a matrix in which the number of rows is equal to the number of columns.
00:07:32A square matrix is a matrix in which the number of rows is equal to the number of columns.
00:07:52A square matrix is a matrix in which the number of rows is equal to the number of columns.
00:08:15Null matrix is a matrix in which the number of rows is equal to the number of columns.
00:08:37A matrix is called a null or zero matrix if each of its entries is zero.
00:09:07A matrix is called a null or zero matrix if each of its entries is zero.
00:09:32A matrix is called a null or zero matrix if each of its entries is zero.
00:09:47A matrix is called a transpose of a matrix.
00:10:15A matrix is called a transpose of a matrix.
00:10:43A matrix is called a transpose of a matrix.
00:10:53A matrix is called a transpose of a matrix.
00:11:23A matrix is called a transpose of a matrix.
00:11:53A matrix is called a transpose of a matrix.
00:12:23A matrix is called a transpose of a matrix.
00:12:53A matrix is called a transpose of a matrix.
00:13:23A matrix is called a transpose of a matrix.
00:13:53A matrix is called a transpose of a matrix.
00:14:23A matrix is called a transpose of a matrix.
00:14:53A matrix is called a transpose of a matrix.
00:15:23A matrix is called a transpose of a matrix.
00:15:53A matrix is called a transpose of a matrix.
00:16:23A matrix is called a transpose of a matrix.
00:16:53A matrix is called a transpose of a matrix.
00:17:05A matrix is called a transpose of a matrix.
00:17:25A matrix is called a transpose of a matrix.
00:17:55A matrix is called a transpose of a matrix.
00:18:25A matrix is called a transpose of a matrix.
00:18:55A matrix is called a transpose of a matrix.
00:19:25A matrix is called a square matrix.
00:19:37A square matrix is symmetric if it is equal to its transpose.
00:20:05A square matrix is symmetric if it is equal to its transpose.
00:20:17A square matrix is symmetric if it is equal to its transpose.
00:20:47A square matrix is symmetric if it is equal to its transpose.
00:20:57A square matrix is symmetric if it is equal to its transpose.
00:21:07A square matrix is symmetric if it is equal to its transpose.
00:21:37A square matrix is symmetric if it is equal to its transpose.
00:21:57A square matrix is symmetric if it is equal to its transpose.
00:22:17A square matrix is symmetric if it is equal to its transpose.
00:22:47A square matrix is symmetric if it is equal to its transpose.
00:23:17A square matrix is symmetric if it is equal to its transpose.
00:23:37A square matrix is symmetric if it is equal to its transpose.
00:24:07A square matrix is symmetric if it is equal to its transpose.
00:24:37A square matrix is symmetric if it is equal to its transpose.
00:25:07A square matrix is symmetric if it is equal to its transpose.
00:25:37A square matrix is symmetric if it is equal to its transpose.
00:26:02A square matrix is symmetric if it is equal to its transpose.
00:26:32A square matrix is symmetric if it is equal to its transpose.
00:27:02A square matrix is symmetric if it is equal to its transpose.
00:27:12A square matrix is symmetric if it is equal to its transpose.
00:27:25A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:27:55A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:28:25A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:28:55A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:29:15A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:29:35A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:30:05A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:30:25A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:30:52A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:31:22A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:31:37A square matrix A is called a diagonal matrix if at least any one of the entries of its diagonal is not 0.
00:31:59A diagonal matrix is called a scalar matrix if all the diagonal entries are same and non-zero.
00:32:27A diagonal matrix is called a scalar matrix if all the diagonal entries are same and non-zero.
00:32:57Identity matrix is called a diagonal matrix if all the diagonal entries are same and non-zero.
00:33:27Identity matrix is called a scalar matrix if all the diagonal entries are same and non-zero.
00:33:52Identity matrix is called a scalar matrix if all the diagonal entries are same and non-zero.
00:34:22Identity matrix is called a scalar matrix if all the diagonal entries are same and non-zero.
00:34:52A matrix is called a row matrix if all the diagonal entries are same and non-zero.
00:35:22A matrix is called a column matrix if all the diagonal entries are same and non-zero.
00:35:52A matrix is called a column matrix if all the diagonal entries are same and non-zero.
00:36:16I hope it was easy for you.
00:36:46I hope it was easy for you.
00:36:48I hope it was easy for you.
00:36:50I hope it was easy for you.
00:36:52I hope it was easy for you.
00:36:54I hope it was easy for you.
00:37:24I hope it was easy for you.
00:37:26I hope it was easy for you.
00:37:28I hope it was easy for you.
00:37:30I hope it was easy for you.
00:37:32I hope it was easy for you.
00:37:34I hope it was easy for you.
00:37:36I hope it was easy for you.
00:37:38I hope it was easy for you.
00:37:40I hope it was easy for you.
00:37:42I hope it was easy for you.
00:37:44I hope it was easy for you.
00:37:46I hope it was easy for you.
00:37:48I hope it was easy for you.
00:37:50I hope it was easy for you.
00:37:52I hope it was easy for you.
00:37:54I hope it was easy for you.
00:37:56I hope it was easy for you.
00:37:58I hope it was easy for you.
00:38:00I hope it was easy for you.
00:38:02I hope it was easy for you.
00:38:04I hope it was easy for you.
00:38:06I hope it was easy for you.
00:38:08I hope it was easy for you.
00:38:10I hope it was easy for you.
00:38:12I hope it was easy for you.
00:38:14I hope it was easy for you.
00:38:16I hope it was easy for you.
00:38:18I hope it was easy for you.
00:38:20I hope it was easy for you.
00:38:22I hope it was easy for you.
00:38:24I hope it was easy for you.
00:38:26I hope it was easy for you.
00:38:28I hope it was easy for you.
00:38:30I hope it was easy for you.
00:38:32I hope it was easy for you.
00:38:34I hope it was easy for you.
00:38:36I hope it was easy for you.
00:38:38I hope it was easy for you.
00:38:40I hope it was easy for you.
00:38:42I hope it was easy for you.
00:38:44I hope it was easy for you.
00:38:46I hope it was easy for you.
00:38:48I hope it was easy for you.
00:38:50I hope it was easy for you.
00:38:52I hope it was easy for you.
00:38:54I hope it was easy for you.
00:38:56I hope it was easy for you.
00:38:58I hope it was easy for you.
00:39:00I hope it was easy for you.
00:39:02I hope it was easy for you.
00:39:04I hope it was easy for you.
00:39:06I hope it was easy for you.
00:39:08I hope it was easy for you.
00:39:10I hope it was easy for you.
00:39:12I hope it was easy for you.
00:39:14I hope it was easy for you.
00:39:16I hope it was easy for you.
00:39:18I hope it was easy for you.
00:39:20I hope it was easy for you.
00:39:22I hope it was easy for you.
00:39:24I hope it was easy for you.
00:39:26I hope it was easy for you.
00:39:28I hope it was easy for you.
00:39:30I hope it was easy for you.
00:39:32I hope it was easy for you.
00:39:34I hope it was easy for you.
00:39:36I hope it was easy for you.
00:39:38I hope it was easy for you.
00:39:40I hope it was easy for you.
00:39:42I hope it was easy for you.
00:39:44I hope it was easy for you.
00:39:46I hope it was easy for you.
00:39:48I hope it was easy for you.
00:39:50I hope it was easy for you.
00:39:52I hope it was easy for you.
00:39:54I hope it was easy for you.
00:39:56I hope it was easy for you.
00:39:58I hope it was easy for you.
00:40:00I hope it was easy for you.
00:40:02I hope it was easy for you.
00:40:04I hope it was easy for you.
00:40:06I hope it was easy for you.
00:40:08I hope it was easy for you.
00:40:10I hope it was easy for you.
00:40:12I hope it was easy for you.
00:40:14I hope it was easy for you.
00:40:16I hope it was easy for you.
00:40:18I hope it was easy for you.
00:40:20I hope it was easy for you.
00:40:22I hope it was easy for you.
00:40:24I hope it was easy for you.
00:40:26I hope it was easy for you.
00:40:28I hope it was easy for you.
00:40:30I hope it was easy for you.
00:40:32I hope it was easy for you.
00:40:34I hope it was easy for you.
00:40:36I hope it was easy for you.
00:40:38I hope it was easy for you.
00:40:40I hope it was easy for you.
00:40:42I hope it was easy for you.
00:40:44I hope it was easy for you.
00:40:46I hope it was easy for you.
00:40:48I hope it was easy for you.
00:40:50I hope it was easy for you.
00:40:52I hope it was easy for you.
00:40:54I hope it was easy for you.
00:40:56I hope it was easy for you.
00:40:58I hope it was easy for you.
00:41:00I hope it was easy for you.
00:41:02I hope it was easy for you.
00:41:04I hope it was easy for you.
00:41:06I hope it was easy for you.
00:41:08I hope it was easy for you.
00:41:10I hope it was easy for you.
00:41:12I hope it was easy for you.
00:41:14I hope it was easy for you.
00:41:16I hope it was easy for you.
00:41:18I hope it was easy for you.
00:41:20I hope it was easy for you.
00:41:22I hope it was easy for you.
00:41:24I hope it was easy for you.
00:41:26I hope it was easy for you.
00:41:28I hope it was easy for you.
00:41:30I hope it was easy for you.
00:41:32I hope it was easy for you.
00:41:34I hope it was easy for you.
00:41:36I hope it was easy for you.
00:41:38I hope it was easy for you.
00:41:40I hope it was easy for you.
00:41:42I hope it was easy for you.
00:41:44I hope it was easy for you.
00:41:46I hope it was easy for you.
00:41:48I hope it was easy for you.
00:41:50I hope it was easy for you.
00:41:52I hope it was easy for you.
00:41:54I hope it was easy for you.
00:41:56I hope it was easy for you.
00:41:58I hope it was easy for you.
00:42:00I hope it was easy for you.
00:42:02I hope it was easy for you.
00:42:04I hope it was easy for you.
00:42:06I hope it was easy for you.
00:42:08I hope it was easy for you.
00:42:10I hope it was easy for you.
00:42:12I hope it was easy for you.
00:42:14I hope it was easy for you.
00:42:16I hope it was easy for you.
00:42:18I hope it was easy for you.
00:42:20I hope it was easy for you.
00:42:22I hope it was easy for you.
00:42:24I hope it was easy for you.
00:42:26I hope it was easy for you.
00:42:28I hope it was easy for you.
00:42:30I hope it was easy for you.
00:42:32I hope it was easy for you.
00:42:34I hope it was easy for you.
00:42:36I hope it was easy for you.
00:42:38I hope it was easy for you.
00:42:40I hope it was easy for you.
00:42:42I hope it was easy for you.
00:42:44I hope it was easy for you.
00:42:46I hope it was easy for you.
00:42:48I hope it was easy for you.
00:42:50I hope it was easy for you.
00:42:52I hope it was easy for you.
00:42:54I hope it was easy for you.
00:42:56I hope it was easy for you.
00:42:58I hope it was easy for you.
00:43:00I hope it was easy for you.
00:43:02I hope it was easy for you.
00:43:04I hope it was easy for you.
00:43:06I hope it was easy for you.
00:43:08I hope it was easy for you.
00:43:10I hope it was easy for you.
00:43:12I hope it was easy for you.
00:43:14I hope it was easy for you.
00:43:16I hope it was easy for you.
00:43:18I hope it was easy for you.
00:43:20I hope it was easy for you.
00:43:22I hope it was easy for you.
00:43:24I hope it was easy for you.
00:43:26I hope it was easy for you.
00:43:28I hope it was easy for you.
00:43:30I hope it was easy for you.
00:43:32I hope it was easy for you.
00:43:34I hope it was easy for you.
00:43:36I hope it was easy for you.
00:43:38I hope it was easy for you.
00:43:40I hope it was easy for you.
00:43:42I hope it was easy for you.
00:43:44I hope it was easy for you.
00:43:46I hope it was easy for you.
00:43:48I hope it was easy for you.
00:43:50I hope it was easy for you.
00:43:52I hope it was easy for you.
00:43:54I hope it was easy for you.
00:43:56I hope it was easy for you.
00:43:58I hope it was easy for you.
00:44:00I hope it was easy for you.
00:44:02I hope it was easy for you.
00:44:04I hope it was easy for you.
00:44:06I hope it was easy for you.
00:44:08I hope it was easy for you.
00:44:10I hope it was easy for you.
00:44:12I hope it was easy for you.
00:44:14I hope it was easy for you.
00:44:16I hope it was easy for you.
00:44:18I hope it was easy for you.
00:44:20I hope it was easy for you.
00:44:22I hope it was easy for you.
00:44:24I hope it was easy for you.
00:44:26I hope it was easy for you.
00:44:28I hope it was easy for you.
00:44:30I hope it was easy for you.
00:44:32I hope it was easy for you.
00:44:34I hope it was easy for you.
00:44:36I hope it was easy for you.
00:44:38I hope it was easy for you.
00:44:40I hope it was easy for you.
00:44:42I hope it was easy for you.
00:44:44I hope it was easy for you.
00:44:46I hope it was easy for you.
00:44:48I hope it was easy for you.
00:44:50I hope it was easy for you.
00:44:52I hope it was easy for you.
00:44:54I hope it was easy for you.
00:44:56I hope it was easy for you.
00:44:58I hope it was easy for you.
00:45:00I hope it was easy for you.
00:45:02I hope it was easy for you.
00:45:04I hope it was easy for you.
00:45:06I hope it was easy for you.
00:45:08I hope it was easy for you.
00:45:10I hope it was easy for you.
00:45:12I hope it was easy for you.
00:45:14I hope it was easy for you.
00:45:16I hope it was easy for you.
00:45:18I hope it was easy for you.
00:45:20I hope it was easy for you.
00:45:22I hope it was easy for you.
00:45:24I hope it was easy for you.
00:45:26I hope it was easy for you.
00:45:28I hope it was easy for you.
00:45:30I hope it was easy for you.
00:45:32I hope it was easy for you.
00:45:34I hope it was easy for you.
00:45:36I hope it was easy for you.
00:45:38I hope it was easy for you.
00:45:40I hope it was easy for you.
00:45:42I hope it was easy for you.
00:45:44I hope it was easy for you.
00:45:46I hope it was easy for you.
00:45:48I hope it was easy for you.
00:45:50I hope it was easy for you.
00:45:52I hope it was easy for you.
00:45:54I hope it was easy for you.
00:45:56I hope it was easy for you.
00:45:58I hope it was easy for you.
00:46:00I hope it was easy for you.
00:46:02I hope it was easy for you.
00:46:04I hope it was easy for you.
00:46:06I hope it was easy for you.
00:46:08I hope it was easy for you.
00:46:10I hope it was easy for you.
00:46:12I hope it was easy for you.
00:46:14I hope it was easy for you.
00:46:16I hope it was easy for you.
00:46:18I hope it was easy for you.
00:46:20I hope it was easy for you.
00:46:22I hope it was easy for you.
00:46:24I hope it was easy for you.
00:46:26I hope it was easy for you.
00:46:28I hope it was easy for you.
00:46:30I hope it was easy for you.
00:46:32I hope it was easy for you.
00:46:34I hope it was easy for you.
00:46:36I hope it was easy for you.
00:46:38I hope it was easy for you.
00:46:40I hope it was easy for you.
00:46:42I hope it was easy for you.
00:46:44I hope it was easy for you.
00:46:46I hope it was easy for you.
00:46:48I hope it was easy for you.
00:46:50I hope it was easy for you.
00:46:52I hope it was easy for you.
00:46:54I hope it was easy for you.
00:46:56I hope it was easy for you.
00:46:58I hope it was easy for you.
00:47:00I hope it was easy for you.
00:47:02I hope it was easy for you.
00:47:04I hope it was easy for you.
00:47:06I hope it was easy for you.
00:47:08I hope it was easy for you.
00:47:10I hope it was easy for you.
00:47:12I hope it was easy for you.
00:47:14I hope it was easy for you.
00:47:16I hope it was easy for you.
00:47:18I hope it was easy for you.
00:47:20I hope it was easy for you.
00:47:22I hope it was easy for you.
00:47:24I hope it was easy for you.
00:47:26I hope it was easy for you.
00:47:28I hope it was easy for you.
00:47:30I hope it was easy for you.
00:47:32I hope it was easy for you.
00:47:34I hope it was easy for you.
00:47:36I hope it was easy for you.
00:47:38I hope it was easy for you.
00:47:40I hope it was easy for you.
00:47:42I hope it was easy for you.
00:47:44I hope it was easy for you.
00:47:46I hope it was easy for you.
00:47:48I hope it was easy for you.
00:47:50I hope it was easy for you.
00:47:52I hope it was easy for you.
00:47:54I hope it was easy for you.
00:47:56I hope it was easy for you.
00:47:58I hope it was easy for you.
00:48:00I hope it was easy for you.
00:48:02I hope it was easy for you.
00:48:04I hope it was easy for you.
00:48:06I hope it was easy for you.
00:48:08I hope it was easy for you.
00:48:10I hope it was easy for you.
00:48:12I hope it was easy for you.
00:48:14I hope it was easy for you.
00:48:16I hope it was easy for you.
00:48:18I hope it was easy for you.
00:48:20I hope it was easy for you.
00:48:22I hope it was easy for you.
00:48:24I hope it was easy for you.
00:48:26I hope it was easy for you.
00:48:28I hope it was easy for you.
00:48:30I hope it was easy for you.
00:48:32I hope it was easy for you.
00:48:34I hope it was easy for you.
00:48:36I hope it was easy for you.
00:48:38I hope it was easy for you.
00:48:40I hope it was easy for you.
00:48:42I hope it was easy for you.
00:48:44I hope it was easy for you.
00:48:46I hope it was easy for you.
00:48:48I hope it was easy for you.
00:48:50I hope it was easy for you.
00:48:52I hope it was easy for you.
00:48:54I hope it was easy for you.
00:48:56I hope it was easy for you.
00:48:58I hope it was easy for you.
00:49:00I hope it was easy for you.
00:49:02I hope it was easy for you.
00:49:04I hope it was easy for you.
00:49:06I hope it was easy for you.
00:49:08I hope it was easy for you.
00:49:10I hope it was easy for you.
00:49:12I hope it was easy for you.
00:49:14I hope it was easy for you.
00:49:16I hope it was easy for you.
00:49:18I hope it was easy for you.
00:49:20I hope it was easy for you.
00:49:22I hope it was easy for you.
00:49:24I hope it was easy for you.
00:49:26I hope it was easy for you.
00:49:28I hope it was easy for you.
00:49:30I hope it was easy for you.
00:49:32I hope it was easy for you.
00:49:34I hope it was easy for you.
00:49:36I hope it was easy for you.
00:49:38I hope it was easy for you.
00:49:40I hope it was easy for you.
00:49:42I hope it was easy for you.
00:49:44I hope it was easy for you.
00:49:46I hope it was easy for you.
00:49:48I hope it was easy for you.
00:49:50I hope it was easy for you.
00:49:52I hope it was easy for you.
00:49:54I hope it was easy for you.
00:49:56I hope it was easy for you.
00:49:58I hope it was easy for you.
00:50:00I hope it was easy for you.
00:50:02I hope it was easy for you.
00:50:04I hope it was easy for you.
00:50:06I hope it was easy for you.
00:50:08I hope it was easy for you.
00:50:10I hope it was easy for you.
00:50:12I hope it was easy for you.
00:50:14I hope it was easy for you.
00:50:16I hope it was easy for you.
00:50:18I hope it was easy for you.
00:50:20I hope it was easy for you.
00:50:22I hope it was easy for you.
00:50:24I hope it was easy for you.
00:50:26I hope it was easy for you.
00:50:28I hope it was easy for you.
00:50:30I hope it was easy for you.
00:50:32I hope it was easy for you.
00:50:34I hope it was easy for you.
00:50:36I hope it was easy for you.
00:50:38I hope it was easy for you.
00:50:40I hope it was easy for you.
00:50:42I hope it was easy for you.
00:50:44I hope it was easy for you.
00:50:46I hope it was easy for you.
00:50:48I hope it was easy for you.
00:50:50I hope it was easy for you.
00:50:52I hope it was easy for you.
00:50:54I hope it was easy for you.
00:50:56I hope it was easy for you.
00:50:58I hope it was easy for you.
00:51:00I hope it was easy for you.
00:51:02I hope it was easy for you.
00:51:04I hope it was easy for you.
00:51:06I hope it was easy for you.
00:51:08I hope it was easy for you.
00:51:10I hope it was easy for you.
00:51:12I hope it was easy for you.
00:51:14I hope it was easy for you.
00:51:16I hope it was easy for you.
00:51:18I hope it was easy for you.
00:51:20I hope it was easy for you.
00:51:22I hope it was easy for you.
00:51:24I hope it was easy for you.
00:51:26I hope it was easy for you.
00:51:28I hope it was easy for you.
00:51:30I hope it was easy for you.
00:51:32I hope it was easy for you.
00:51:34I hope it was easy for you.
00:51:36I hope it was easy for you.
00:51:38I hope it was easy for you.
00:51:40I hope it was easy for you.
00:51:42I hope it was easy for you.
00:51:44I hope it was easy for you.
00:51:46I hope it was easy for you.
00:51:48I hope it was easy for you.
00:51:50I hope it was easy for you.
00:51:52I hope it was easy for you.
00:51:54I hope it was easy for you.
00:51:56I hope it was easy for you.
00:51:58I hope it was easy for you.
00:52:00I hope it was easy for you.
00:52:02I hope it was easy for you.
00:52:04I hope it was easy for you.
00:52:06I hope it was easy for you.
00:52:08I hope it was easy for you.
00:52:10I hope it was easy for you.
00:52:12I hope it was easy for you.
00:52:14I hope it was easy for you.
00:52:16I hope it was easy for you.
00:52:18I hope it was easy for you.
00:52:20I hope it was easy for you.
00:52:22I hope it was easy for you.
00:52:24I hope it was easy for you.
00:52:26I hope it was easy for you.
00:52:28I hope it was easy for you.
00:52:30I hope it was easy for you.
00:52:32I hope it was easy for you.
00:52:34I hope it was easy for you.
00:52:36I hope it was easy for you.
00:52:38I hope it was easy for you.
00:52:40I hope it was easy for you.
00:52:42I hope it was easy for you.
00:52:44I hope it was easy for you.
00:52:46I hope it was easy for you.
00:52:48I hope it was easy for you.
00:52:50I hope it was easy for you.
00:52:52I hope it was easy for you.
00:52:54I hope it was easy for you.
00:52:56I hope it was easy for you.
00:52:58I hope it was easy for you.
00:53:00I hope it was easy for you.
00:53:02I hope it was easy for you.
00:53:04I hope it was easy for you.
00:53:06I hope it was easy for you.
00:53:08I hope it was easy for you.
00:53:10I hope it was easy for you.
00:53:12I hope it was easy for you.
00:53:14I hope it was easy for you.
00:53:16I hope it was easy for you.
00:53:18I hope it was easy for you.
00:53:20I hope it was easy for you.
00:53:22I hope it was easy for you.
00:53:24I hope it was easy for you.
00:53:26I hope it was easy for you.
00:53:28I hope it was easy for you.
00:53:30I hope it was easy for you.
00:53:32I hope it was easy for you.
00:53:34I hope it was easy for you.
00:53:36I hope it was easy for you.
00:53:38I hope it was easy for you.
00:53:40I hope it was easy for you.
00:53:42I hope it was easy for you.
00:53:44I hope it was easy for you.
00:53:46I hope it was easy for you.
00:53:48I hope it was easy for you.
00:53:50I hope it was easy for you.
00:53:52I hope it was easy for you.
00:53:54I hope it was easy for you.
00:53:56I hope it was easy for you.
00:53:58I hope it was easy for you.
00:54:00I hope it was easy for you.
00:54:02I hope it was easy for you.
00:54:04I hope it was easy for you.
00:54:06I hope it was easy for you.
00:54:08I hope it was easy for you.
00:54:10I hope it was easy for you.
00:54:12I hope it was easy for you.
00:54:14I hope it was easy for you.
00:54:16I hope it was easy for you.
00:54:18I hope it was easy for you.
00:54:20I hope it was easy for you.
00:54:22I hope it was easy for you.
00:54:24I hope it was easy for you.
00:54:26I hope it was easy for you.
00:54:28I hope it was easy for you.
00:54:30I hope it was easy for you.
00:54:32I hope it was easy for you.
00:54:34I hope it was easy for you.
00:54:36I hope it was easy for you.
00:54:38I hope it was easy for you.
00:54:40I hope it was easy for you.
00:54:42I hope it was easy for you.
00:54:44I hope it was easy for you.
00:54:46I hope it was easy for you.
00:54:48I hope it was easy for you.
00:54:50I hope it was easy for you.
00:54:52I hope it was easy for you.
00:54:54I hope it was easy for you.
00:54:56I hope it was easy for you.
00:54:58I hope it was easy for you.
00:55:00I hope it was easy for you.
00:55:02I hope it was easy for you.
00:55:04I hope it was easy for you.
00:55:06I hope it was easy for you.
00:55:08I hope it was easy for you.
00:55:10I hope it was easy for you.
00:55:12I hope it was easy for you.
00:55:14I hope it was easy for you.
00:55:16I hope it was easy for you.
00:55:18I hope it was easy for you.
00:55:20I hope it was easy for you.
00:55:22I hope it was easy for you.
00:55:24I hope it was easy for you.
00:55:26I hope it was easy for you.
00:55:28I hope it was easy for you.
00:55:30I hope it was easy for you.
00:55:32I hope it was easy for you.
00:55:34I hope it was easy for you.
00:55:36I hope it was easy for you.
00:55:38I hope it was easy for you.
00:55:40I hope it was easy for you.
00:55:42I hope it was easy for you.
00:55:44I hope it was easy for you.
00:55:46I hope it was easy for you.
00:55:48I hope it was easy for you.
00:55:50I hope it was easy for you.
00:55:52I hope it was easy for you.
00:55:54I hope it was easy for you.
00:55:56I hope it was easy for you.
00:55:58I hope it was easy for you.
00:56:00I hope it was easy for you.
00:56:02I hope it was easy for you.
00:56:04I hope it was easy for you.
00:56:06I hope it was easy for you.
00:56:08I hope it was easy for you.
00:56:10I hope it was easy for you.
00:56:12I hope it was easy for you.
00:56:14I hope it was easy for you.
00:56:16I hope it was easy for you.
00:56:18I hope it was easy for you.
00:56:20I hope it was easy for you.
00:56:22I hope it was easy for you.
00:56:24I hope it was easy for you.
00:56:26I hope it was easy for you.
00:56:28I hope it was easy for you.
00:56:30I hope it was easy for you.
00:56:32I hope it was easy for you.
00:56:34I hope it was easy for you.
00:56:36I hope it was easy for you.
00:56:38I hope it was easy for you.
00:56:40I hope it was easy for you.
00:56:42I hope it was easy for you.
00:56:44I hope it was easy for you.
00:56:46I hope it was easy for you.
00:56:48I hope it was easy for you.
00:56:50I hope it was easy for you.
00:56:52I hope it was easy for you.
00:56:54I hope it was easy for you.
00:56:56I hope it was easy for you.
00:56:58I hope it was easy for you.
00:57:00I hope it was easy for you.
00:57:02I hope it was easy for you.
00:57:04I hope it was easy for you.
00:57:06I hope it was easy for you.
00:57:08I hope it was easy for you.
00:57:10I hope it was easy for you.
00:57:12I hope it was easy for you.
00:57:14I hope it was easy for you.
00:57:16I hope it was easy for you.
00:57:18I hope it was easy for you.
00:57:20I hope it was easy for you.
00:57:22I hope it was easy for you.
00:57:24I hope it was easy for you.
00:57:26I hope it was easy for you.
00:57:28I hope it was easy for you.
00:57:30I hope it was easy for you.
00:57:32I hope it was easy for you.
00:57:34I hope it was easy for you.
00:57:36I hope it was easy for you.
00:57:38I hope it was easy for you.
00:57:40I hope it was easy for you.
00:57:42I hope it was easy for you.
00:57:44I hope it was easy for you.
00:57:46I hope it was easy for you.
00:57:48I hope it was easy for you.
00:57:50I hope it was easy for you.
00:57:52I hope it was easy for you.
00:57:54I hope it was easy for you.
00:57:56I hope it was easy for you.
00:57:58I hope it was easy for you.
00:58:00I hope it was easy for you.
00:58:02I hope it was easy for you.
00:58:04I hope it was easy for you.
00:58:06I hope it was easy for you.
00:58:08I hope it was easy for you.
00:58:10I hope it was easy for you.
00:58:12I hope it was easy for you.
00:58:14I hope it was easy for you.
00:58:16I hope it was easy for you.
00:58:18I hope it was easy for you.
00:58:20I hope it was easy for you.
00:58:22I hope it was easy for you.
00:58:24I hope it was easy for you.
00:58:26I hope it was easy for you.
00:58:28I hope it was easy for you.
00:58:30I hope it was easy for you.
00:58:32I hope it was easy for you.
00:58:34I hope it was easy for you.
00:58:36I hope it was easy for you.
00:58:38I hope it was easy for you.
00:58:40I hope it was easy for you.
00:58:42I hope it was easy for you.
00:58:44I hope it was easy for you.
00:58:46I hope it was easy for you.
00:58:48I hope it was easy for you.
00:58:50I hope it was easy for you.
00:58:52I hope it was easy for you.
00:58:54I hope it was easy for you.
00:58:56I hope it was easy for you.
00:58:58I hope it was easy for you.
00:59:00I hope it was easy for you.
00:59:02I hope it was easy for you.
00:59:04I hope it was easy for you.
00:59:06I hope it was easy for you.
00:59:08I hope it was easy for you.
00:59:10I hope it was easy for you.
00:59:12I hope it was easy for you.
00:59:14I hope it was easy for you.
00:59:16I hope it was easy for you.
00:59:18I hope it was easy for you.
00:59:20I hope it was easy for you.
00:59:22I hope it was easy for you.
00:59:24I hope it was easy for you.
00:59:26I hope it was easy for you.
00:59:28I hope it was easy for you.
00:59:30I hope it was easy for you.
00:59:32I hope it was easy for you.
00:59:34I hope it was easy for you.
00:59:36I hope it was easy for you.
00:59:38I hope it was easy for you.
00:59:40I hope it was easy for you.
00:59:42I hope it was easy for you.
00:59:44I hope it was easy for you.
00:59:46I hope it was easy for you.
00:59:48I hope it was easy for you.
00:59:50I hope it was easy for you.
00:59:52I hope it was easy for you.
00:59:54I hope it was easy for you.
00:59:56I hope it was easy for you.
00:59:58I hope it was easy for you.
01:00:00I hope it was easy for you.
01:00:02I hope it was easy for you.
01:00:04I hope it was easy for you.
01:00:06I hope it was easy for you.
01:00:08I hope it was easy for you.
01:00:10I hope it was easy for you.
01:00:12I hope it was easy for you.
01:00:14I hope it was easy for you.
01:00:16I hope it was easy for you.
01:00:18I hope it was easy for you.
01:00:20I hope it was easy for you.
01:00:22I hope it was easy for you.
01:00:24I hope it was easy for you.
01:00:26I hope it was easy for you.
01:00:28I hope it was easy for you.
01:00:30I hope it was easy for you.
01:00:32I hope it was easy for you.
01:00:34I hope it was easy for you.
01:00:36I hope it was easy for you.
01:00:38I hope it was easy for you.
01:00:40I hope it was easy for you.
01:00:42I hope it was easy for you.
01:00:44I hope it was easy for you.
01:00:46I hope it was easy for you.
01:00:48I hope it was easy for you.
01:00:50I hope it was easy for you.
01:00:52I hope it was easy for you.
01:00:54I hope it was easy for you.
01:00:56I hope it was easy for you.
01:00:58I hope it was easy for you.
01:01:00I hope it was easy for you.
01:01:02I hope it was easy for you.
01:01:04I hope it was easy for you.
01:01:06I hope it was easy for you.
01:01:08I hope it was easy for you.
01:01:10I hope it was easy for you.
01:01:12I hope it was easy for you.
01:01:14I hope it was easy for you.
01:01:16I hope it was easy for you.
01:01:18I hope it was easy for you.
01:01:20I hope it was easy for you.
01:01:22I hope it was easy for you.
01:01:24I hope it was easy for you.
01:01:26I hope it was easy for you.
01:01:28I hope it was easy for you.
01:01:30I hope it was easy for you.
01:01:32I hope it was easy for you.
01:01:34I hope it was easy for you.
01:01:36I hope it was easy for you.
01:01:38I hope it was easy for you.
01:01:40I hope it was easy for you.
01:01:42I hope it was easy for you.
01:01:44I hope it was easy for you.
01:01:46I hope it was easy for you.
01:01:48I hope it was easy for you.
01:01:50I hope it was easy for you.
01:01:52I hope it was easy for you.
01:01:54I hope it was easy for you.
01:01:56I hope it was easy for you.
01:01:58I hope it was easy for you.
01:02:00I hope it was easy for you.
01:02:02I hope it was easy for you.
01:02:04I hope it was easy for you.
01:02:06I hope it was easy for you.
01:02:08I hope it was easy for you.
01:02:10I hope it was easy for you.
01:02:12I hope it was easy for you.
01:02:14I hope it was easy for you.
01:02:16I hope it was easy for you.
01:02:18I hope it was easy for you.
01:02:20I hope it was easy for you.
01:02:22I hope it was easy for you.
01:02:24I hope it was easy for you.
01:02:26I hope it was easy for you.
01:02:28I hope it was easy for you.
01:02:30I hope it was easy for you.
01:02:32I hope it was easy for you.
01:02:34I hope it was easy for you.
01:02:36I hope it was easy for you.
01:02:38I hope it was easy for you.
01:02:40I hope it was easy for you.
01:02:42I hope it was easy for you.
01:02:44I hope it was easy for you.
01:02:46I hope it was easy for you.
01:02:48I hope it was easy for you.
01:02:50I hope it was easy for you.
01:02:52I hope it was easy for you.
01:02:54I hope it was easy for you.
01:02:56I hope it was easy for you.
01:02:58I hope it was easy for you.
01:03:00I hope it was easy for you.
01:03:02I hope it was easy for you.
01:03:04I hope it was easy for you.
01:03:06I hope it was easy for you.
01:03:08I hope it was easy for you.
01:03:10I hope it was easy for you.
01:03:12I hope it was easy for you.
01:03:14I hope it was easy for you.
01:03:16I hope it was easy for you.
01:03:18I hope it was easy for you.
01:03:20I hope it was easy for you.
01:03:22I hope it was easy for you.
01:03:24I hope it was easy for you.
01:03:26I hope it was easy for you.
01:03:28I hope it was easy for you.
01:03:30I hope it was easy for you.
01:03:32I hope it was easy for you.
01:03:34I hope it was easy for you.
01:03:36I hope it was easy for you.
01:03:38I hope it was easy for you.
01:03:40I hope it was easy for you.
01:03:42I hope it was easy for you.
01:03:44I hope it was easy for you.
01:03:46I hope it was easy for you.
01:03:48I hope it was easy for you.
01:03:50I hope it was easy for you.
01:03:52I hope it was easy for you.
01:03:54I hope it was easy for you.
01:03:56I hope it was easy for you.
01:03:58I hope it was easy for you.
01:04:00I hope it was easy for you.
01:04:02I hope it was easy for you.
01:04:04I hope it was easy for you.
01:04:06I hope it was easy for you.
01:04:08I hope it was easy for you.
01:04:10I hope it was easy for you.
01:04:12I hope it was easy for you.
01:04:14I hope it was easy for you.
01:04:16I hope it was easy for you.
01:04:18I hope it was easy for you.
01:04:20I hope it was easy for you.
01:04:22I hope it was easy for you.
01:04:24I hope it was easy for you.
01:04:26I hope it was easy for you.
01:04:28I hope it was easy for you.
01:04:30I hope it was easy for you.
01:04:32I hope it was easy for you.
01:04:34I hope it was easy for you.
01:04:36I hope it was easy for you.
01:04:38I hope it was easy for you.
01:04:40I hope it was easy for you.
01:04:42I hope it was easy for you.
01:04:44I hope it was easy for you.
01:04:46I hope it was easy for you.
01:04:48I hope it was easy for you.
01:04:50I hope it was easy for you.
01:04:52I hope it was easy for you.
01:04:54I hope it was easy for you.
01:04:56I hope it was easy for you.
01:04:58I hope it was easy for you.
01:05:00I hope it was easy for you.
01:05:02I hope it was easy for you.
01:05:04I hope it was easy for you.
01:05:06I hope it was easy for you.
01:05:08I hope it was easy for you.
01:05:10I hope it was easy for you.
01:05:12I hope it was easy for you.
01:05:14I hope it was easy for you.
01:05:16I hope it was easy for you.
01:05:18I hope it was easy for you.
01:05:20I hope it was easy for you.
01:05:22I hope it was easy for you.
01:05:24I hope it was easy for you.
01:05:26I hope it was easy for you.
01:05:28I hope it was easy for you.
01:05:30I hope it was easy for you.
01:05:32I hope it was easy for you.
01:05:34I hope it was easy for you.
01:05:36I hope it was easy for you.
01:05:38I hope it was easy for you.
01:05:40I hope it was easy for you.
01:05:42I hope it was easy for you.
01:05:44I hope it was easy for you.
01:05:46I hope it was easy for you.
01:05:48I hope it was easy for you.
01:05:50I hope it was easy for you.
01:05:52I hope it was easy for you.
01:05:54I hope it was easy for you.
01:05:56I hope it was easy for you.
01:05:58I hope it was easy for you.
01:06:00I hope it was easy for you.
01:06:02I hope it was easy for you.
01:06:04I hope it was easy for you.
01:06:06I hope it was easy for you.
01:06:08I hope it was easy for you.
01:06:10I hope it was easy for you.
01:06:12I hope it was easy for you.
01:06:14I hope it was easy for you.
01:06:16I hope it was easy for you.
01:06:18I hope it was easy for you.
01:06:20I hope it was easy for you.
01:06:22I hope it was easy for you.
01:06:24I hope it was easy for you.
01:06:26I hope it was easy for you.
01:06:28I hope it was easy for you.
01:06:30I hope it was easy for you.
01:06:32I hope it was easy for you.
01:06:34I hope it was easy for you.
01:06:36I hope it was easy for you.
01:06:38I hope it was easy for you.
01:06:40I hope it was easy for you.
01:06:42I hope it was easy for you.
01:06:44I hope it was easy for you.
01:06:46I hope it was easy for you.
01:06:48I hope it was easy for you.
01:06:50I hope it was easy for you.
01:06:52I hope it was easy for you.
01:06:54I hope it was easy for you.
01:06:56I hope it was easy for you.
01:06:58I hope it was easy for you.
01:07:00I hope it was easy for you.
01:07:02I hope it was easy for you.
01:07:04I hope it was easy for you.
01:07:06I hope it was easy for you.
01:07:08I hope it was easy for you.
01:07:10I hope it was easy for you.
01:07:12I hope it was easy for you.
01:07:14I hope it was easy for you.
01:07:16I hope it was easy for you.
01:07:18I hope it was easy for you.
01:07:20I hope it was easy for you.
01:07:22I hope it was easy for you.
01:07:24I hope it was easy for you.
01:07:26I hope it was easy for you.
01:07:28I hope it was easy for you.
01:07:30I hope it was easy for you.
01:07:32I hope it was easy for you.
01:07:34I hope it was easy for you.
01:07:36I hope it was easy for you.
01:07:38I hope it was easy for you.
01:07:40I hope it was easy for you.
01:07:42I hope it was easy for you.
01:07:44I hope it was easy for you.
01:07:46I hope it was easy for you.
01:07:48I hope it was easy for you.
01:07:50I hope it was easy for you.
01:07:52I hope it was easy for you.
01:07:54I hope it was easy for you.
01:07:56I hope it was easy for you.
01:07:58I hope it was easy for you.
01:08:00I hope it was easy for you.
01:08:02I hope it was easy for you.
01:08:04I hope it was easy for you.
01:08:06I hope it was easy for you.
01:08:08I hope it was easy for you.
01:08:10I hope it was easy for you.
01:08:12I hope it was easy for you.
01:08:14I hope it was easy for you.
01:08:16I hope it was easy for you.
01:08:18I hope it was easy for you.
01:08:20I hope it was easy for you.
01:08:22I hope it was easy for you.
01:08:24I hope it was easy for you.
01:08:26I hope it was easy for you.
01:08:28I hope it was easy for you.
01:08:30I hope it was easy for you.
01:08:32I hope it was easy for you.
01:08:34I hope it was easy for you.
01:08:36I hope it was easy for you.
01:08:38I hope it was easy for you.
01:08:40I hope it was easy for you.
01:08:42I hope it was easy for you.
01:08:44I hope it was easy for you.
01:08:46I hope it was easy for you.
01:08:48I hope it was easy for you.
01:08:50I hope it was easy for you.
01:08:52I hope it was easy for you.
01:08:54I hope it was easy for you.
01:08:56I hope it was easy for you.
01:08:58I hope it was easy for you.
01:09:00I hope it was easy for you.
01:09:02I hope it was easy for you.
01:09:04I hope it was easy for you.
01:09:06I hope it was easy for you.
01:09:08I hope it was easy for you.
01:09:10I hope it was easy for you.
01:09:12I hope it was easy for you.
01:09:14I hope it was easy for you.
01:09:16I hope it was easy for you.
01:09:18I hope it was easy for you.
01:09:20I hope it was easy for you.
01:09:22I hope it was easy for you.
01:09:24I hope it was easy for you.
01:09:26I hope it was easy for you.
01:09:28I hope it was easy for you.
01:09:30I hope it was easy for you.
01:09:32I hope it was easy for you.
01:09:34I hope it was easy for you.
01:09:36I hope it was easy for you.
01:09:38I hope it was easy for you.
01:09:40I hope it was easy for you.
01:09:42I hope it was easy for you.
01:09:44I hope it was easy for you.
01:09:46I hope it was easy for you.
01:09:48I hope it was easy for you.
01:09:50I hope it was easy for you.
01:09:52I hope it was easy for you.
01:09:54I hope it was easy for you.
01:09:56I hope it was easy for you.
01:09:58I hope it was easy for you.
01:10:00I hope it was easy for you.
01:10:02I hope it was easy for you.
01:10:04I hope it was easy for you.
01:10:06I hope it was easy for you.
01:10:08I hope it was easy for you.
01:10:10I hope it was easy for you.
01:10:12I hope it was easy for you.
01:10:14I hope it was easy for you.
01:10:16I hope it was easy for you.
01:10:18I hope it was easy for you.
01:10:20I hope it was easy for you.
01:10:22I hope it was easy for you.
01:10:24I hope it was easy for you.
01:10:26I hope it was easy for you.
01:10:28I hope it was easy for you.
01:10:30I hope it was easy for you.
01:10:32I hope it was easy for you.
01:10:34I hope it was easy for you.
01:10:36I hope it was easy for you.
01:10:38I hope it was easy for you.
01:10:40I hope it was easy for you.
01:10:42I hope it was easy for you.
01:10:44I hope it was easy for you.
01:10:46I hope it was easy for you.
01:10:48I hope it was easy for you.
01:10:50I hope it was easy for you.
01:10:52I hope it was easy for you.
01:10:54I hope it was easy for you.
01:10:56I hope it was easy for you.
01:10:58I hope it was easy for you.