Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Find all $2 \times 2$ matrices A such that $adj (A) = A^{T}$ .

Therefore, the $adj (A) = A^{T}$ is given by,

$A = [\begin{matrix} a & b \\ - b & a \end{matrix}]$ .

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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 “.”

Step 2: To find adj(A)=AT.

Let,

$A = [\begin{matrix} a & b \\ c & d \end{matrix}]$

Then, we have

$A^{T} = [\begin{matrix} a & c \\ b & d \end{matrix}]$ ,

and

$adj A = [\begin{matrix} d & - b \\ - c & a \end{matrix}]$

For $A^{T} = adj A$ , we need $a = d$ and $b = - c$ .

Thus,

$A = [\begin{matrix} a & b \\ - b & a \end{matrix}]$ .

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Linear Algebra With Applications

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Short Answer

Find all $2 \times 2$ matrices A such that $adj (A) = A^{T}$ .

Step by Step Solution

Step 1: Matrix Definition.

Step 2: To find adj(A)=AT.

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Linear Algebra With Applications

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Short Answer

Find all 2×2 matrices A such that adj(A)=AT.

Step by Step Solution

Step 1: Matrix Definition.

Step 2: To find adj(A)=AT.

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Find all $2 \times 2$ matrices A such that $adj (A) = A^{T}$ .