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 624: 11

Answer

a. $\left[\begin{array}{ll} 3 & 2\\ 6 & 2\\ 5 & 7 \end{array}\right]$ b. $\left[\begin{array}{ll} -1 & 4\\ 0 & 6\\ 5 & 5 \end{array}\right]$ c. $\left[\begin{array}{ll} -4 & -12\\ -12 & -16\\ -20 & -24 \end{array}\right]$ d. $\left[\begin{array}{ll} 7 & 7\\ 15 & 8\\ 15 & 20 \end{array}\right]$

Work Step by Step

a. $A+B=\left[\begin{array}{ll} 1+2 & 3-1\\ 3+3 & 4-2\\ 5+0 & 6+1 \end{array}\right]=\left[\begin{array}{ll} 3 & 2\\ 6 & 2\\ 5 & 7 \end{array}\right]$ b. $A-B=\left[\begin{array}{ll} 1-2 & 3-(-1)\\ 3-3 & 4-(-2)\\ 5-0 & 6-1 \end{array}\right]=\left[\begin{array}{ll} -1 & 4\\ 0 & 6\\ 5 & 5 \end{array}\right]$ c. $-4A=\left[\begin{array}{ll} -4(1) & -4(3)\\ -4(3) & -4(4)\\ -4(5) & -4(6) \end{array}\right]=\left[\begin{array}{ll} -4 & -12\\ -12 & -16\\ -20 & -24 \end{array}\right]$ d. $3A+2B=\left[\begin{array}{ll} 3(1)+2(2) & 3(3)+2(-1)\\ 3(3)+2(3) & 3(4)+2(-2)\\ 3(5)+2(0) & 3(6)+2(1) \end{array}\right]=\left[\begin{array}{ll} 7 & 7\\ 15 & 8\\ 15 & 20 \end{array}\right]$
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