  ### Home > PC3 > Chapter 9 > Lesson 9.1.3 > Problem9-62

9-62.

Given the matrices listed below, complete the operations specified.

$A = \left[ \begin{array} { c c c } { 2 } & { 4 } & { - 1 } \\ { 3 } & { 0 } & { 2 } \end{array} \right]$ $\quad B = \left[ \begin{array} { c c } { 3 } & { 1 } \\ { - 2 } & { - 1 } \end{array} \right]$$\quad C = \left[ \begin{array} { r } { 3 } \\ { - 2 } \\ { 4 } \end{array} \right]$$\quad D = \left[ \begin{array} { c c } { 1 } & { 1 } \\ { - 2 } & { - 3 } \end{array} \right]$

1. $B + D$

$\begin{bmatrix}3+1&1+1\\-2+(-2)&-1+(-3)\end{bmatrix}$

1. $2A$

Double each entry in matrix $A$.

1. $AC$

Multiply each row in matrix $A$ by the column in matrix $C$.

$\begin{bmatrix}2(3)+4(-2)+(-1)(4)\\3(3)+0(-2)+2(4)\end{bmatrix}$

1. $CA$

Do the rows of matrix $C$ have the same number of entries as the columns of matrix $A$?

1. $BD$

Multiply the rows of matrix $B$ by the columns of matrix $D$.

1. What does the result in part (e) tell you about matrices $B$ and $D$?

$M\cdot M^{-1}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$