Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

If the determinant of a $2 \times 2$ matrix is 4, then the inequality $| |A \vec{v}| | \leq 4 | |\vec{v}| |$ must hold for all vectors $\vec{v}$ in .

Therefore, the given statement is true.

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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

Let,

$A = [\begin{matrix} 4 & 4 \\ 0 & 1 \end{matrix}]$ .

Clearly,

det A = 4 , however, for

$V = [\begin{matrix} 1 \\ 1 \end{matrix}]$

We have,

$||A v|| = ||[[\begin{matrix} 8 \\ 1 \end{matrix}]]|| ||A v|| = \sqrt{65} > \sqrt{32} ||A v|| = 4 ||v||$

Therefore, the given statement is true.

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Linear Algebra With Applications

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Short Answer

If the determinant of a $2 \times 2$ matrix is 4, then the inequality $| |A \vec{v}| | \leq 4 | |\vec{v}| |$ must hold for all vectors $\vec{v}$ in .

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

If the determinant of a 2×2 matrix is 4, then the inequality |Av→|≤4|v→| must hold for all vectors v→ in .

Step by Step Solution

Step 1: Matrix Definition

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

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If the determinant of a $2 \times 2$ matrix is 4, then the inequality $| |A \vec{v}| | \leq 4 | |\vec{v}| |$ must hold for all vectors $\vec{v}$ in .