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Found in: Page 308

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# ${\mathbit{d}}{\mathbit{e}}{\mathbit{t}}\left(4A\right){\mathbf{=}}{\mathbf{4}}{\mathbit{d}}{\mathbit{e}}{\mathbit{t}}{\mathbit{A}}$ for all ${\mathbf{4}}{\mathbf{×}}{\mathbf{4}}$ matrices A.

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

See the step by step solution

## 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,

$detA=1$.

But,

$det4A=det4I=16\ne 4detA$ .

We get,

$det\left(4A\right)={4}^{4}\mathrm{d}\mathrm{et}\left(A\right)$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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