College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.3: 28

Answer

a. $AB=\left[\begin{array}{ll} -10 & 12\\ 25 & -30 \end{array}\right]$ b. $BA=\left[\begin{array}{ll} 0 & 0\\ 9 & -40 \end{array}\right]$

Work Step by Step

The product of an $m\times\underline{n}$ matrix $A$ and an $\underline{n}\times p$ matrix $B$ is an $m\times p$ matrix $AB$. The element in the ith row and $j\mathrm{t}\mathrm{h}$ column of $AB$ is found by multiplying each element in the ith row of $A$ by the corresponding element in the $j\mathrm{t}\mathrm{h}$ column of $B$ and adding the products. ----------------- a. $A$ is a $2\times\underline{2}$ matrix, B is a $\underline{2}\times 2$ matrix $AB$ exists, and is a 2$\times$2 matrix. $AB=\left[\begin{array}{ll} 3(0)+(-2)(5) & 3(0)+(-2)(-6)\\ 1(0)+5(5) & 1(0)+5(-6) \end{array}\right]=\left[\begin{array}{ll} -10 & 12\\ 25 & -30 \end{array}\right]$ b. $B$ is a $2\times\underline{2}$ matrix, $A$ is a $\underline{2}\times 2$ matrix $BA$ exists, and is a 2$\times$2 matrix. $BA=\left[\begin{array}{ll} 0(3)+0(1) & 0(-2)+0(5)\\ 5(3)+(-6)(1) & 5(-2)+(-6)(5 \end{array}\right]=\left[\begin{array}{ll} 0 & 0\\ 9 & -40 \end{array}\right]$
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