Answered: A = 2. 2.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter5: Linear Inequalities

Section5.2: Solving Inequalities By Multiplication And Division

Problem 3AGP

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Question

Determine whether the matrix is symmetric, orthogonal, both, or neither.

Expert Solution

Step 1

The given matrix is $A = [\begin{matrix} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \end{matrix}]$ .

We have to check whether the given matrix is symmetric and orthogonal or not.

Step 2

The matrix is symmetric if $A^{T} = A$ .

$A = [\begin{matrix} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \end{matrix}]$

The transpose of the matrix A is $A^{T} = [\begin{matrix} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \end{matrix}]$ .

Since, $A^{T} = A$

Therefore A is a symmetric matrix.

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