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Question
Compute $AB^T$ if
$\begin{equation*}A=\begin{bmatrix}3&&1&&2&&4\\1&&5&&6&&2\end{bmatrix},B=\begin{bmatrix}4&&0\\ 2&&5\\ 1&&3\\ 0&&2 \end{bmatrix}\end{equation*}$
Solution
VerifiedStep 1
1 of 2$\begin{align*} AB^T &= \begin{bmatrix} 3 & 1 & 2 & 4\\ 1 & 5 & 6 & 2\end{bmatrix} \begin{bmatrix} 4 & 0 \\ 2 & 5\\ 1 & 3\\ 0 & 2\\ \end{bmatrix}^T\\ &=\begin{bmatrix} 3 & 1 & 2 & 4\\ 1 & 5 & 6 & 2\end{bmatrix} \begin{bmatrix} 4 & 2 & 1 & 0\\ 0 & 5 & 3 & 2\end{bmatrix}\\ &=\begin{bmatrix} 7 & 3 & 3 & 4\\ 1 & 0 & 3 & 4\end{bmatrix} \end{align*}$

The transpose of a matrix is found by swapping rows as corresponding columns (or vice versa).

Addition or subtraction of matrices is done by adding or subtracting corresponding components.
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