(b) Consider the following system of equations in which x, Y and z are threeinterdependent variables:10X -3Y - 5Z 10-2X+Y 5-X- 5Y + 10Z = 3(1)Write the system of equations in matrix form.(H)Using Cramer's rule, find the equilibrium values of X, Y and Z.

Answered: Image /qna-images/answer/1769f196-0b14-4edb-8527-a39154f26ca5.jpg

Answered: (b) Consider the following system of…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

3. Consider the system of linear equations AF = 5, where (a) Determine A- (b) Use A- to find F in a+ ib form.
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
Consider the following system of equations: 2x+y=z=8 3x - 2y + 3z = 23 3x - 2y z=7 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: C = det (A) 8 12 B α 1-9 -7 where a and 3 are parameters. If matrix C is the inverse of matrix A (C = A−¹), what are the values of a and B? -1 (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.
Use the inverse of the coefficient matrix to solve the system of equations. x+2y+3z = 9 2x+3y + 4z = -13 -x-2y-4z = 2 (x,y,z)=(.. (Type an ordered triple, using integers or fractions.)
2. a) Given the following system of linear equations: -6+ 10 *+y+=5 2x-y+=9 x-2y+3z =16 Detemine the values of x, y and z using the Cramer's rule.

Recommended textbooks for you

Algebra and Trigonometry (6th Edition)

Algebra

ISBN:

9780134463216

Author:

Robert F. Blitzer

Publisher:

PEARSON

Contemporary Abstract Algebra

Algebra

ISBN:

9781305657960

Author:

Joseph Gallian

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (6th Edition)

Algebra

ISBN:

9780134463216

Author:

Robert F. Blitzer

Publisher:

PEARSON

Contemporary Abstract Algebra

Algebra

ISBN:

9781305657960

Author:

Joseph Gallian

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra And Trigonometry (11th Edition)

Algebra

ISBN:

9780135163078

Author:

Michael Sullivan

Publisher:

PEARSON

Introduction to Linear Algebra, Fifth Edition

Algebra

ISBN:

9780980232776

Author:

Gilbert Strang

Publisher:

Wellesley-Cambridge Press

College Algebra (Collegiate Math)

Algebra

ISBN:

9780077836344

Author:

Julie Miller, Donna Gerken

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS

(b) Consider the following system of equations in which x, y and z are three interdependent variables: 10X-3Y - 5Zz = 10 -2X +Y = 5 -X-5Y + 10Z 3 (1) Write the system of equations in matrix form. (H) Using Cramer's rule, find the equilibrium values of X, Y and Z.