Exercise · ZW-MATRIX-MULTIPLICATION-007 · ★★☆ Intermediate
Compute \(A\mathbf v\) for \(A=\begin{pmatrix}1&2&0\\0&1&-1\end{pmatrix}\) and \(\mathbf v=\begin{pmatrix}2\\1\\3\end{pmatrix}\).
Choose one option.
A \(\begin{pmatrix}4\\2\end{pmatrix}\) B \(\begin{pmatrix}2\\-2\end{pmatrix}\) C \(\begin{pmatrix}0\\-2\end{pmatrix}\) D \(\begin{pmatrix}4\\-2\end{pmatrix}\) Show answer D. \(\begin{pmatrix}4\\-2\end{pmatrix}\)← Back to the question
Explanation Each row of \(A\) is multiplied by \(\mathbf v\): \(2+2+0=4\) and \(0+1-3=-2\).
The product \(AB\) of two matrices \(A\) and \(B\), when \(A\) has as many columns as \(B\) has rows, is the matrix whose \((i,j)\) entry combines row \(i\) of \(A\) with column \(j\) of \(B\).
\[(AB)_{ij}=\sum_{k=1}^{n}a_{ik}b_{kj}\]
More practice problems: matrix multiplication