Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - Problems - Page 135: 5

Answer

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Work Step by Step

$ABC=\begin{bmatrix} -3 & 2 & 7 &-1\\6 & 0 &-3 & -5 \end{bmatrix}\begin{bmatrix} -2 &8\\8& -3\\-1 & -9\\0 &2 \end{bmatrix}\begin{bmatrix} -6 &1\\1 &5 \end{bmatrix}\\=\begin{bmatrix} 15 &-95\\-9 & 65 \end{bmatrix}\begin{bmatrix} -6&1\\1&5 \end{bmatrix}\\ =\begin{bmatrix} -185 &-460\\119 &316 \end{bmatrix}$ $CAB=\begin{bmatrix} -6 &1\\1 &5 \end{bmatrix}\begin{bmatrix} -3 & 2 & 7 &-1\\6 & 0 &-3 & -5 \end{bmatrix}\begin{bmatrix} -2 &8\\8& -3\\-1 & -9\\0 &2 \end{bmatrix}\\=\begin{bmatrix} 24 & -12 &-45 &1\\27 & 2&-8 &-26 \end{bmatrix}\begin{bmatrix} -2 &8\\8&-3\\-1 & -9\\0 & 2 \end{bmatrix}\\ =\begin{bmatrix} -99 & 635 \\95 &196 \end{bmatrix}$
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