Question 3 Consider the following system of equations: 2x+ 4y +5z 7 X - 3y-3z -11 -2x + 4y-2z = 22 where x, y, and z are the amounts of the three goods produced in the ecor system of equations will give us the equilibrium output for each good. T 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 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 c matrix singular or nonsingular? Can we find the inverse of this coefficien Explain your reasoning. (c) Consider the following matrix: 28 3 C = det (A) 6. 11 -2 –16 where a and are parameters. If matrix C is the inverse of matrix A (C what are the values of a and 8? (d) Using the inverse of the coefficients matrix A- that you calculated in the part, solve for the (unknown) variables c, y, and z.

Question 3 Consider the following system of equations: 2x+ 4y +5z 7 X - 3y-3z -11 -2x + 4y-2z = 22 where x, y, and z are the amounts of the three goods produced in the ecor system of equations will give us the equilibrium output for each good. T 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 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 c matrix singular or nonsingular? Can we find the inverse of this coefficien Explain your reasoning. (c) Consider the following matrix: 28 3 C = det (A) 6. 11 -2 –16 where a and are parameters. If matrix C is the inverse of matrix A (C what are the values of a and 8? (d) Using the inverse of the coefficients matrix A- that you calculated in the part, solve for the (unknown) variables c, 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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