Answered: Suppose A · B = 0. Show that this…

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Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.2: Matrix Algebra

Problem 21EQ: Prove the half of Theorem 3.3 (e) that was not proved in the text.

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Question

Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

Expert Solution

Step 1

Suppose A.B = 0 then we have to show that

Column space of B contained in the null space of A

i.e C(B) is contained in Null(A)

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