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Question

# Compute $A-B^T$ 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

Verified
Step 1
1 of 2

\begin{align*} A-B^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*}

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

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

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