CPM Homework Help : A2C Problem 11-136

Given the matrices $A$ , $B$ , and $C$ shown below, calculate each of the following (if possible).

$AB$
Hint (a):
Multiply the appropriate rows into the columns and then add.
Answer (a):
$\begin{bmatrix}20 & 19 & 4 \\ 23 & 7 & -2 \end{bmatrix}$

$BA$
Hint (b):
Is the number of columns in the first matrix equal to the number or rows in the second matrix?
Answer (b):
Not possible.

$2A + C$
Hint (c):
Find $2A$ before adding $C$ .
Answer (c):
$\begin{bmatrix} 1 & 6\\0 & 11 \end{bmatrix}$

$AC − A$
Hint (d):
Find $AC$ before adding $A$ .
Answer (d):
$\begin{bmatrix} -2 & 6 \\ 12 & 8 \end{bmatrix}$

$\left. \begin{array} { c } { A = \left[ \begin{array} { c c } { 2 } & { 3 } \\ { - 1 } & { 4 } \end{array} \right] } \\ { B = \left[ \begin{array} { c c c } { 1 } & { 5 } & { 2 } \\ { 6 } & { 3 } & { 0 } \end{array} \right] } \\ { C = \left[ \begin{array} { r r } { - 3 } & { 0 } \\ { 2 } & { 3 } \end{array} \right] } \end{array} \right.$