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Q15E

Expert-verified

Found in: Page 263

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Question: TRUE OR FALSE? If matrices A and B are commute, then A must commute $B^{T}$ with as well.

The given statement is false.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of a commute.

Suppose A and B are two matrices.

Then the matrices A and B re said to be commute if AB = BA

Step 2: Check whether the given statement is a true or false.

The given statement is if matrices A and B are commute, the A must commute with $B^{T}$ as well.

It is know that the matrix multiplication is not commutative.

So, $A B^{T} = B^{T} A$ is not true always.

Then the given statement is false.

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Find the length of each of the vectors In exercises 1 through 3.

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If the nxn matrices A and B are orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well? $B^{- 1} AB$ .

TRUE OR FALSE? If $\overset{⇀}{x} a n d \overset{⇀}{y}$ are two vectors in $R^{n}$ , then the equation role="math" localid="1659506190737" $∥ \vec{x} + \vec{y} ∥^{2} = ∥ \vec{x} ∥^{2} + ∥ \vec{y} ∥^{2}$ must hold.

If the $n \times n$ matrices A and B are orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well?AB.

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Linear Algebra With Applications

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Short Answer

Question: TRUE OR FALSE? If matrices A and B are commute, then A must commute $B^{T}$ with as well.

Step by Step Solution

Step 1: Definition of a commute.

Step 2: Check whether the given statement is a true or false.

Most popular questions for Math Textbooks

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Linear Algebra With Applications

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Short Answer

Question: TRUE OR FALSE? If matrices A and B are commute, then A must commute BT with as well.

Step by Step Solution

Step 1: Definition of a commute.

Step 2: Check whether the given statement is a true or false.

Most popular questions for Math Textbooks

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Question: TRUE OR FALSE? If matrices A and B are commute, then A must commute $B^{T}$ with as well.