CPM Homework Help : PC Problem 12-43

Given the matrices listed below, complete the operations specified.

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

$B + D$
Step (a):
$\begin{bmatrix}3+1&1+1\\-2+(-2)&-1+(-3)\end{bmatrix}$

$2A$
Hint (b):
Double each entry in matrix $A$ .

$AC$
Hint (c):
Multiply each row in matrix $A$ by the column in matrix $C$ .
Step (c):
$\begin{bmatrix}2(3)+4(-2)+(-1)(4)\\3(3)+0(-2)+2(4)\end{bmatrix}$

$CA$
Hint (d):
Do the rows of matrix $C$ have the same number of entries as the columns of matrix $A$ ?

$BD$
Hint (e):
Multiply the rows of matrix $B$ by the columns of matrix $D$ .

What does the result in part (e) tell you about matrices $B$ and $D$ ?
Hint (f):
$M\cdot M^{-1}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$