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Q13E

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Found in: Page 233

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

If the nxn matrices A and B are symmetric and B is invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well? 3A.

The Matrix 3A is symmetric.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of symmetric matrix.

A square matrix is symmetric matrix if $A = A - T$

Step 2: Verification whether the given matrix is symmetric.

Given that A and B are symmetric matrices and B is invertible.

Since A is symmetric, then $A = A^{T}$ .

Then by properties of transpose, $(kA) = {kA}^{T}$ it gives,

${(3 A)}^{T} = 3 A^{T} = 3 A$

Therefore, 3A is a symmetric matrix.

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Linear Algebra With Applications

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Short Answer

If the nxn matrices A and B are symmetric and B is invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well? 3A.

Step by Step Solution

Step 1: Definition of symmetric matrix.

Step 2: Verification whether the given matrix is symmetric.

Most popular questions for Math Textbooks

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Linear Algebra With Applications

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Short Answer

If the nxn matrices A and B are symmetric and B is invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well? 3A.

Step by Step Solution

Step 1: Definition of symmetric matrix.

Step 2: Verification whether the given matrix is symmetric.

Most popular questions for Math Textbooks

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