Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

$d e t (4 A) = 4 d e t A$ for all $4 \times 4$ matrices A.

Therefore, the given condition is not satisfied. So, the given statement is false.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition.

A determinant is a unique number associated with a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

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

For example, if

$A = I$

then,

$d e t A = 1$ .

But,

$d e t 4 A = d e t 4 I = 16 \neq 4 d e t A$ .

We get,

$d e t (4 A) = 4^{4} d et (A)$ because, all the four columns are multiplied by 4.

Therefore, the given condition is not satisfied. So, the given statement is false.

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Linear Algebra With Applications

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Short Answer

$d e t (4 A) = 4 d e t A$ for all $4 \times 4$ matrices A.

Step by Step Solution

Step 1: 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

det(4A)=4detA for all 4×4 matrices A.

Step by Step Solution

Step 1: Definition.

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

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$d e t (4 A) = 4 d e t A$ for all $4 \times 4$ matrices A.