Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.5 Perform Basic Matrix Operations - 3.5 Exercises - Skill Practice - Page 191: 18


$$\begin{bmatrix} 2&-4 \\ 18&-4 \end{bmatrix}$$

Work Step by Step

Using the distributive property for matrices, martix A becomes: $$\begin{bmatrix} 20&-16 \\ 12 &-4 \end{bmatrix}$$ We know that to add matrices, one must add each of the components to the corresponding components of the other matrix. For instance, in the form of a 2 by 2 matrix: $\begin{bmatrix} a & b \\ c&d\end{bmatrix}$ + $\begin{bmatrix} e& f \\ g&h \end{bmatrix}$=$\begin{bmatrix} a +e& b+f \\ c+g &d +h\end{bmatrix}$ Note, while a two by two matrix is shown, this also works for matrices of all sizes. The same process also works for subtraction, multiplication, and division. Performing this operation for the given matrix, we obtain: $$\begin{bmatrix} 2&-4 \\ 18&-4 \end{bmatrix}$$
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