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ECO606 Assignment No 2 Solution Autumn 2021-VU-Mathematical Economics

Question No. 1
10p1 - p2 -p3 = 35
-p1 + 2p2 -4p3 = 30
-p1-p2+3p3= 25

Given the above set of equations, extract the coefficient matrix and find out
its determinant.

Question No. 2
Assume three sectors in an economy; agriculture (x), industry (y), and services (z). (I-A) shows Leontief matrix and D shows consumer demand.
Find out the output level for agriculture, industry, and service sector by using the above information.
Transcript
00:00Assalamualaikum dear students and viewers, welcome to my YouTube channel DG Learner Point.
00:06In today's video tutorial, we will solve Mathematical Economics 1 subject code ECO 606 with number 2
00:15which is related to autumn semester 2021.
00:18Its due date is 30th December 2021.
00:21Its marks are 10 and it has 2 questions and 5 marks for each question.
00:27Before we start the tutorial, I request you to subscribe to my channel.
00:35Also, if you or your friends want to take online tutorship, we will provide it.
00:42I will tell you how to contact us in detail in the next video.
00:49So, let's start the tutorial.
00:5110P1-P2-P3 is equal to 35-P1-P2-P3 is equal to 30-P1-P2-P3 is equal to 25
01:01So, I will suppose that this is a question related to demand and price.
01:11Given the above set of equations, extract the coefficient matrix.
01:17We have to extract the coefficient matrix and find out its determinant.
01:25Let's solve this first and then we will go to the next question.
01:32So, the first question is the solution.
01:36Before that, you have the information that if you want to take online tutorship services from us,
01:42then you can message us on WhatsApp number plus 92-331-5547438
01:48or you can email us and take any query or information about it.
01:55So, we have the solution 1.
01:57I have not kept the set of 3 equations to save time.
02:03So, what are the coefficients?
02:05We call the multiples of P as coefficients.
02:08So, we have taken it as 10-1-1.
02:11I will also show you.
02:1310-1-1
02:1510-1-1
02:1710-1-1
02:1910-1-1
02:2110-1-1
02:2310-1-1
02:2510-1-1
02:2710-1-1
02:2910-1-1
02:3110-1-1
02:3310-1-1
02:3510-1-1
02:3710-1-1
02:3910-1-1
02:42Let's keep the values of the first row and make it the first column.
02:47So, what will happen to us?
02:49The first element of it, we took it out.
02:52After that, we have the matrix left.
02:542-4-1-3
02:56Then, what do we have?
02:57Minus comes.
02:58Now, we don't have to try in minus.
03:00We will take the first row and the second column.
03:06So, the first element of the second column and the first row is minus 1.
03:10We took it out.
03:11This is the minus formula.
03:12This is the minus values.
03:13What do we have?
03:15Minus 1, minus 4, minus 1, 3.
03:18Then, we have the last.
03:20Plus, minus and then plus.
03:22According to this formula.
03:23And the minus with the values is minus.
03:27So, we have the first row and the third column.
03:29And what did we do in the third column?
03:32We took the first element out.
03:34Then, we have the matrix left.
03:36Minus 1, 2, minus 1, minus 1, minus 1, 2, minus 1, minus 1.
03:41We have to take the determinant out.
03:42Determinant of A is equal to 10.
03:452 into 3 is 6.
03:47Minus, minus, plus.
03:48Then, minus.
03:49So, we have minus into plus.
03:52Minus will become minus 4 plus.
03:54This becomes minus minus plus.
03:56What will come inside?
03:58Minus 1 into 3, minus 3.
04:00Then, minus into minus 1, minus 4.
04:06Plus into minus, minus.
04:09Minus 4 will come.
04:10Minus.
04:11This will convert plus into minus.
04:13Minus will become minus 1 into minus 1, plus 1.
04:16Then, we have minus.
04:19Minus into minus 2, plus 2 will come.
04:21So, what will we have?
04:2320.
04:246 minus 4, 2.
04:262 into 10, 10.
04:282 into 10, 20.
04:30Minus, minus 3, minus 4, minus 7.
04:33Then, what will we have?
04:36Minus into 3.
04:38So, we have the determinant of A.
04:40The coefficient of matrix is 10.
04:43Here, I would like to make one more request.
04:45If I have made any mistake in the calculation or in anything.
04:48Then, you must share it in the comment section.
04:51So that, all students and viewers can be saved from that mistake.
04:55And, all will be well.
04:56If you want to discuss at any point.
04:59Then, in the comment section.
05:01With your thoughts or questions.
05:04You can drop it.
05:06So that, we can discuss it.
05:08And, we can make it a more satisfactory solution.
05:11But, I still believe here.
05:13Question number 2.
05:14Now, we will go to question number 2.
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