Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 12 - Matrices - 12-1 Adding and Subtracting Matrices - Practice and Problem-Solving Exercises - Page 768: 8

Answer

$\begin{bmatrix} 2 & 1 & 2 \\ 1 & 2 & 1 \end{bmatrix} - \begin{bmatrix} 2 & 3 & 2 \\ 3 & 2 & 3 \end{bmatrix} = \begin{bmatrix} 0 & -2 & 0 \\ -2 & 0 & -2 \end{bmatrix}$

Work Step by Step

Adding/subtracting the corresponding elements, the given matrix expression $ \begin{bmatrix} 2 & 1 & 2 \\ 1 & 2 & 1 \end{bmatrix} - \begin{bmatrix} 2 & 3 & 2 \\ 3 & 2 & 3 \end{bmatrix} ,$ simplifies to \begin{align*} & \begin{bmatrix} 2-2 & 1-3 & 2-2 \\ 1-3 & 2-2 & 1 -3 \end{bmatrix} \\\\&= \begin{bmatrix} 0 & -2 & 0 \\ -2 & 0 & -2 \end{bmatrix} .\end{align*} Hence, $ \begin{bmatrix} 2 & 1 & 2 \\ 1 & 2 & 1 \end{bmatrix} - \begin{bmatrix} 2 & 3 & 2 \\ 3 & 2 & 3 \end{bmatrix} = \begin{bmatrix} 0 & -2 & 0 \\ -2 & 0 & -2 \end{bmatrix} $.
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