(d) Using the inverse of the coefficients matrix A-1 that you calculated in the previous part, solve for the (unknown) variables x, y, and z.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 1DE
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Just need answer to 3d

Question 3
Consider the following system of equations:
2x + 4y + 5z = 7
х — Зу — 32 3 -11
-2x + 4y – 2z = 22
where x, y, and z are the amounts of the three goods produced in the economy. This
system of equations will give us the equilibrium output for each good. To find the
solution to this system of equations, we will carry out the following steps:
(a) Let A denote the matrix for the coefficients in the system and b denote the vector
of the right-hand sides. Write down A and b and their dimensions.
(b) Calculate the determinant det(A) of the coefficients matrix. Is this coefficients
matrix singular or nonsingular? Can we find the inverse of this coefficients matrix?
Explain your reasoning.
(c) Consider the following matrix:
28
3
C =
8
det(A)
11
-2 -16 В
where a and B are parameters. If matrix C is the inverse of matrix A (C = A-'),
what are the values of a and 3?
(d) Using the inverse of the coefficients matrix A-l that you calculated in the previous
part, solve for the (unknown) variables r, y, and z.
Transcribed Image Text:Question 3 Consider the following system of equations: 2x + 4y + 5z = 7 х — Зу — 32 3 -11 -2x + 4y – 2z = 22 where x, y, and z are the amounts of the three goods produced in the economy. This system of equations will give us the equilibrium output for each good. To find the solution to this system of equations, we will carry out the following steps: (a) Let A denote the matrix for the coefficients in the system and b denote the vector of the right-hand sides. Write down A and b and their dimensions. (b) Calculate the determinant det(A) of the coefficients matrix. Is this coefficients matrix singular or nonsingular? Can we find the inverse of this coefficients matrix? Explain your reasoning. (c) Consider the following matrix: 28 3 C = 8 det(A) 11 -2 -16 В where a and B are parameters. If matrix C is the inverse of matrix A (C = A-'), what are the values of a and 3? (d) Using the inverse of the coefficients matrix A-l that you calculated in the previous part, solve for the (unknown) variables r, y, and z.
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