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Linear Algebra and its Applications

Found in: Page 93

Book edition 5th

Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald

Pages 483 pages

ISBN 978-03219822384

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Short Answer

Suppose the last column of AB is entirely zero but B itself has no column of zeros. What can you say about the columns of A?

The columns of A are linearly dependent.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The last column of AB is zero

Consider \({b_p}\) to be the last column of B. The last column of \(AB\) should be zero, according to the hypothesis.

Step 2: Determine the columns of A

Here, \(A{b_p} = 0\). On the other hand, B contains no column of zeros; therefore, \({b_p}\) is not the zero vector. The equation \(A{b_p} = 0\) represents the linear dependence relation among the columns of A.

Thus, the columns of A are linearly dependent.

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