15 ) good handwriting please Let A be a 3 × 3 matrix with two pivot positions. Does the equation Ax = bhave at least one solution for every possible b? Explain.O No. Since A has three rows and two pivots, there is a row without a pivot. Tohave at least one solution for every possible b, all rows of A must have a pivot.O Yes. A has a free variable. So the free variable can equal any value such thatthere is at least one solution for every possible b.O No. A has one free variable, so there will be no solution to the system for anypossible b.Yes. Since A has three rows and two pivots, there is a row without a pivot. Sothere is at least one solution for every possible b.

Given A is a 3×3 matrix with two pivot positions. To find if the equation Ax=b has at least one…

Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = have at least one solution for every possible b? Explain. No. Since A has three rows and two pivots, there is a row withou I have at least one solution for every norcill

Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = have at least one solution for every possible b? Explain. No. Since A has three rows and two pivots, there is a row withou I have at least one solution for every norcill

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 42EQ

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Question

15 ) good handwriting please

Let A be a 3 × 3 matrix with two pivot positions. Does the equation Ax = b
have at least one solution for every possible b? Explain.
O No. Since A has three rows and two pivots, there is a row without a pivot. To
have at least one solution for every possible b, all rows of A must have a pivot.
O Yes. A has a free variable. So the free variable can equal any value such that
there is at least one solution for every possible b.
O No. A has one free variable, so there will be no solution to the system for any
possible b.
Yes. Since A has three rows and two pivots, there is a row without a pivot. So
there is at least one solution for every possible b.

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