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 - Page 625: 46

Answer

$ \left[\begin{array}{ll} 0 & 0\\ 0 & 0 \end{array}\right]$

Work Step by Step

All the matrices are 2$\times$2. The sums and differences are 2$\times$2 matrices, The product of two 2$\times$2 matrices is a 2$\times$2 matrix. $A-B=\left[\begin{array}{ll} 1-1 & 0-0\\ 0-0 & 1-(-1) \end{array}\right]=\left[\begin{array}{ll} 0 & 0\\ 0 & 2 \end{array}\right]$ $C+D=\left[\begin{array}{ll} -1+(-1) & 0+0\\ 0+0 & 1+(-1) \end{array}\right]=\left[\begin{array}{ll} -2 & 0\\ 0 & 0 \end{array}\right]$ $(A-B)(C+D)=\left[\begin{array}{ll} 0 & 0\\ 0 & 2 \end{array}\right]\left[\begin{array}{ll} -2 & 0\\ 0 & 0 \end{array}\right]$ $=\left[\begin{array}{ll} 0+0 & 0+0\\ 0+0 & 0+0 \end{array}\right]$ $=\left[\begin{array}{ll} 0 & 0\\ 0 & 0 \end{array}\right]$
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