Answered: The reduced matrix for a system of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...

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The reduced matrix for a system of equations is given.

1	0	-8	4
0	1	9	5
0	0	0	0

(a)

Identify the type of solution for the system (unique solution, no solution, or infinitely many solutions). Explain your reasoning.

The system has a unique solution because the coefficient array is an identity matrix.

The system has no solution because the coefficient array is not an identity matrix and has a row of zeros with a nonzero entry in the augment.

The system has no solution because the coefficient array is not an identity matrix and doesn't have a row of zeros with a nonzero entry in the augment.

The system has infinitely many solutions because the coefficient array is not an identity matrix and has a row of zeros with a nonzero entry in the augment.

The system has infinitely many solutions because the coefficient array is not an identity matrix and doesn't have a row of zeros with a nonzero entry in the augment.

(b)

For each system that has a solution, find it. If the system has infinitely many solutions, find the general solution in terms of x, y, and z. (If there is no solution, enter NO SOLUTION.)

(x, y, z) =

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