6.
[tex]\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}[/tex]
[tex]a_{1,2}[/tex] is the entry of the matrix above in the 1st row and 2nd column, so [tex]a_{1,2}=2[/tex] (B).
12.
[tex]\begin{bmatrix}5\\-2\\1\end{bmatrix}\begin{bmatrix}1&2\end{bmatrix}=\begin{bmatrix}5\begin{bmatrix}1&2\end{bmatrix}\\-2\begin{bmatrix}1&2\end{bmatrix}\\1\begin{bmatrix}1&2\end{bmatrix}\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}\begin{bmatrix}5&2\end{bmatrix}\\\begin{bmatrix}-2&-4\end{bmatrix}\\\begin{bmatrix}1&2\end{bmatrix}\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}5&10\\-2&-4\\1&2\end{bmatrix}[/tex]
13.
[tex]\begin{bmatrix}-2&0\\0&8\\2&1\end{bmatrix}\begin{bmatrix}12&0&\frac32\\1&-6&7\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}-2&0\end{bmatrix}\begin{bmatrix}12\\1\end{bmatrix}&\begin{bmatrix}-2&0\end{bmatrix}\begin{bmatrix}0\\-6\end{bmatrix}&\begin{bmatrix}-2&0\end{bmatrix}\begin{bmatrix}\frac32\\7\end{bmatrix}\\\begin{bmatrix}0&8\end{bmatrix}\begin{bmatrix}12\\1\end{bmatrix}&\begin{bmatrix}0&8\end{bmatrix}\begin{bmatrix}0\\-6\end{bmatrix}&\begin{bmatrix}0&8\end{bmatrix}\begin{bmatrix}\frac32\\7\end{bmatrix}\\\begin{bmatrix}2&1\end{bmatrix}\begin{bmatrix}12\\1\end{bmatrix}&\begin{bmatrix}2&1\end{bmatrix}\begin{bmatrix}0\\-6\end{bmatrix}&\begin{bmatrix}2&1\end{bmatrix}\begin{bmatrix}\frac32\\7\end{bmatrix}\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}\begin{bmatrix}-24\end{bmatrix}&\begin{bmatrix}0\end{bmatrix}&\begin{bmatrix}-3\end{bmatrix}\\\begin{bmatrix}8\end{bmatrix}&\begin{bmatrix}-48\end{bmatrix}&\begin{bmatrix}56\end{bmatrix}\\\begin{bmatrix}25\end{bmatrix}&\begin{bmatrix}-6\end{bmatrix}&\begin{bmatrix}10\end{bmatrix}\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-24&0&-3\\8&-48&56\\25&-6&10\end{bmatrix}[/tex]
15.
[tex]\begin{vmatrix}-4&-4&-3\\3&3&-5\\-5&2&-5\end{vmatrix}=-4\begin{vmatrix}3&-5\\2&-5\end{vmatrix}-3\begin{vmatrix}-4&-3\\2&-5\end{vmatrix}-5\begin{vmatrix}-4&-3\\3&-5\end{vmatrix}[/tex]
[tex]=-4(3(-5)-2(-5))-3((-4)(-5)-2(-3))-5((-4)(-5)-3(-3))[/tex]
[tex]=-203[/tex]
18.
[tex]\begin{bmatrix}1&-4\\3&5\end{bmatrix}+\begin{bmatrix}-2&6\\-2&4\end{bmatrix}=\begin{bmatrix}1-2&-4+6\\3-2&5+4\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-1&2\\1&9\end{bmatrix}[/tex]
