College Algebra, Chapter 7, 7.2, Section 7.2, Problem 14

Evaluate $ \left[ \begin{array}{cc}
2 & -3 \\
0 & 1 \\
1 & 2
\end{array} \right]
\left[ \begin{array}{c}
5 \\
1
\end{array} \right]$ or explain why it can not be performed.



$
\begin{equation}
\begin{aligned}

& \text{Entry} && \text{Inner Product of} &&& \text{Value} &&&& \text{Matrix}
\\
\\
& C_{11} && \left[ \begin{array}{cc}
2 & -3 \\
0 & 1 \\
1 & 2
\end{array} \right]

\left[ \begin{array}{c}
5 \\
1
\end{array} \right]

&&& 2 \cdot 5 + (-3) \cdot 1 = 7
&&&& \left[ \begin{array}{cc}
7 & \\
&
\end{array}
\right]

\\
\\
\\
\\

& C_{21} && \left[ \begin{array}{cc}
2 & -3 \\
0 & 1 \\
1 & 2
\end{array} \right]

\left[ \begin{array}{c}
5 \\
1
\end{array} \right]

&&& 0 \cdot 5 + 1 \cdot 1 = 1
&&&& \left[ \begin{array}{c}
7 \\
1 \\

\end{array}
\right]

\\
\\
\\
\\

& C_{31}
&& \left[ \begin{array}{cc}
2 & -3 \\
0 & 1 \\
1 & 2
\end{array} \right]

\left[ \begin{array}{c}
5 \\
1
\end{array} \right]

&&& 1 \cdot 5 + 1 \cdot 1 = 6
&&&& \left[ \begin{array}{c}
7 \\
1 \\
6
\end{array}
\right]


\end{aligned}
\end{equation}
$