### Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem9-97

9-97.

Given $C = \left[ \begin{array} { c c } { 3 } & { - 2 } \\ { - 5 } & { 1 } \end{array} \right] , D = \left[ \begin{array} { c c } { 0 } & { 3 } \\ { 4 } & { - 3 } \end{array} \right]$ find:

1. $CD$

Multiply each row of the first matrix into each column of the second matrix.

$\left[ \begin{array} { c c } { - 8 } & { 15 } \\ { 4 } & { - 18 } \end{array} \right]$

1. $C + D$

Add the numbers in the corresponding entries.

$\left[ \begin{array} { c c } { 3 } & { 1 } \\ { - 1 } & { - 2 } \end{array} \right]$

1. $C^{2}$

C 2 = C · C

$\left[ \begin{array} { c c } { 19 } & { - 8 } \\ { - 20 } & { 11 } \end{array} \right]$

1. $X \text{ if } 2X + C = D$

2X + C = D
2X = D − C

$\textit{X}= \frac{(\textit{D}-\textit{C})}{2}$

$\left[ \begin{array} { c c } { - 1.5 } & { 2.5 } \\ { 4.5 } & { - 2 } \end{array} \right]$