College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.4 - Matrix Algebra - 8.4 Assess Your Understanding - Page 598: 18

Answer

$\left[\begin{array}{ccc} {14}&{7}&{-2}\\ {20}&{12}&{-4}\\ {-14}&{7}&{-6}\end{array}\right]$

Work Step by Step

C is a 3 by 2 matrix. B is a 2 by 3 matrix. CB is defined and is a 3 by 3 matrix, the entry $[CB]_{ij}$ = (row i of C)$\times$(column j of B) $CB=\left[\begin{array}{ll} 4 & 1\\ 6 & 2\\ -2 & 3 \end{array}\right]\left[\begin{array}{lll} 4 & 1 & 0\\ -2 & 3 & -2 \end{array}\right]$ $=\left[\begin{array}{ccc} {4(4)+1(-2)}&{4(1)+1(3)}&{4(0)+1(-2)}\\ {6(4)+2(-2)}&{6(1)+2(3)}&{6(0)+2(-2)}\\ {-2(4)+3(-2)}&{-2(1)+3(3)}&{-2(0)+3(-2)}\end{array}\right]$ $=\left[\begin{array}{ccc} {14}&{7}&{-2}\\ {20}&{12}&{-4}\\ {-14}&{7}&{-6}\end{array}\right]$
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