With A=[1 2; 0 1] and B=[3 0; 1 2], compute (AB)^T.

Exercise · ZW-TRANSPOSE-MATRIX-006 · ★★☆ Intermediate

With \(A=\begin{pmatrix}1 & 2 \\ 0 & 1\end{pmatrix}\) and \(B=\begin{pmatrix}3 & 0 \\ 1 & 2\end{pmatrix}\), compute \((AB)^T\).

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C. \(\begin{pmatrix}5 & 1 \\ 4 & 2\end{pmatrix}\)

Explanation

First \(AB=\begin{pmatrix}5 & 4\\ 1 & 2\end{pmatrix}\), then transpose: \(\begin{pmatrix}5 & 1\\ 4 & 2\end{pmatrix}\). It equals \(B^TA^T\); \(A^TB^T\) gives a different result because order matters.

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Review the concept: Transpose matrix

The transpose \(A^T\) of a matrix \(A\) is the one obtained by exchanging its rows and columns.

\[(A^T)_{ij}=a_{ji}\]

With \(A=\begin{pmatrix}1 & 2 \\ 0 & 1\end{pmatrix}\) and \(B=\begin{pmatrix}3 & 0 \\ 1 & 2\end{pmatrix}\), compute \((AB)^T\).

Explanation

Review the concept: Transpose matrix

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