### Home > PC3 > Chapter 10 > Lesson 10.1.5 > Problem10-102

10-102.

Complete the following operations with matrices.

1. $\left[ \begin{array} { l } { - 5 } \\ { - 6 } \end{array} \right] \left[ \begin{array} { c c c } { - 1 } & { 8 } & { 7 } \end{array} \right]$

This is a $2 × 1 · 1 × 3$, so the product matrix is $2 × 3$.

2. $\left[ \begin{array} { c c } { - 10 } & { - 6 } \\ { 3 } & { 4 } \end{array} \right] ^ { - 1 }$

$\left[ \begin{array} { c c } { a } & { b} \\ { c } & { d } \end{array} \right] ^ { - 1 } = \frac{1}{ad-bc}\left[ \begin{array} { c c } { d } & { -b} \\ { c } & { a } \end{array} \right]$

3. Solve $X$: $\left[ \begin{array} { c c c } { - 6 } & { 5 } & { 7 } \\ { - 6 } & { 7 } & { 0 } \end{array} \right] + 2 X = \left[ \begin{array} { r r r } { - 8 } & { - 5 } & { 7 } \\ { 3 } & { - 9 } & { 7 } \end{array} \right]$

$\left[ \begin{array} { c c c } { - 8-6(-6) } & { -5 - 5 } & { 7-7 } \\ { 3-(-6) } & { -9-7 } & { 7-0 } \end{array} \right]$