Example2.2.6

Given the matrices

\begin{equation*} A = \left[\begin{array}{rr} 4 \amp 2 \\ 0 \amp 1 \\ -3 \amp 4 \\ 2 \amp 0 \\ \end{array}\right], B = \left[\begin{array}{rrr} -2 \amp 3 \amp 0 \\ 1 \amp 2 \amp -2 \\ \end{array}\right] \text{,} \end{equation*}

we have

\begin{equation*} AB = \left[\begin{array}{rrr} A \twovec{-2}{1} \amp A \twovec{3}{2} \amp A \twovec{0}{-2} \end{array}\right] = \left[\begin{array}{rrr} -6 \amp 16 \amp -4 \\ 1 \amp 2 \amp -2 \\ 10 \amp -1 \amp -8 \\ -4 \amp 6 \amp 0 \end{array}\right] \text{.} \end{equation*}
in-context