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Q17E

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Linear Algebra With Applications

Found in: Page 309

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

If two $n \times n$ matrices A and B are similar, then the equation $d e t A = d e t B$ must hold.

Therefore, the given condition is satisfied. So, the given statement is true.

See the step by step solution

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.

If A and B are similar, then there exists an invertible matrix T such that,

$A = T^{- 1} B T$

So,

$d e t A = d e t^{- 1} d e t B d e t T d e t A = \frac{1}{d e t T} d e t B d e t T d e t A = d e t B$

Therefore, the given condition is satisfied. So, the given statement is true.

Most popular questions for Math Textbooks

Show that $A (adjA) = 0 = (adjA) A$ for all noninvertible $n \times n$ matrices A. See Exercise 42.

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