Algebra 2 (1st Edition)

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

Chapter 3 Linear Systems and Matrices - Chapter Test - Page 227: 19


$\begin{bmatrix} -26&-22\\ -54&-13 \end{bmatrix}$

Work Step by Step

If the dimensions of matrix A are $a\times b$ and the dimensions of matrix C are $c\times d$, then AC is defined if $b=c$, and then AC has dimensions $a\times d.$ Hence here: $AC=\begin{bmatrix} 1\cdot-6+(-2)\cdot10&1\cdot8+(-2)\cdot15\\ 4\cdot-6+(-3)\cdot10&4\cdot8+(-3)\cdot15 \end{bmatrix} =\begin{bmatrix} -26&-22\\ -54&-13 \end{bmatrix}$
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