Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

There exist real invertible $3 \times 3$ matrices A and S such that .

Therefore, the given statement is not satisfied.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Matrix Definition

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “ $m \times n$ .”

Step 2: To check whether the given condition is true or false

On taking determinant

$d e t (S) d e t (A) d e t (S^{T}) = {(- 1)}^{3} d e t (A) - {(d e t (S))}^{2} d e t A = d e t (A)$ ,

Which is false, as det(S) turns out to be imaginary.

The question is whether there exists an invertible $3 \times 3$ matrix A such that A and 2A are similar. If they were similar, it would have to apply

det A = det(-A)

det A = - detA,

Which, since $d e t A \neq 0$ , is a contradiction. Therefore, the given statement is not satisfied.

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Linear Algebra With Applications

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Short Answer

There exist real invertible $3 \times 3$ matrices A and S such that .

Step by Step Solution

Step 1: Matrix Definition

Step 2: To check whether the given condition is true or false

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Linear Algebra With Applications

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Short Answer

There exist real invertible 3×3 matrices A and S such that .

Step by Step Solution

Step 1: Matrix Definition

Step 2: To check whether the given condition is true or false

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There exist real invertible $3 \times 3$ matrices A and S such that .