If A^T= 3&4 -1&2 0&1 and B= -1&2&1 1&2&3 , find A^T - B^T. - Vidyadip

Question

If $\text{A}^\text{T}=\begin{bmatrix}3&4\\-1&2\\0&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}-1&2&1\\1&2&3\end{bmatrix},$ find $A^T - B^T.$

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Answer

Given: $\text{A}^\text{T}=\begin{bmatrix}3&4\\-1&2\\0&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}-1&2&1\\1&2&3\end{bmatrix}$
$\text{B}^\text{T}=\begin{bmatrix}-1&1\\2&2\\1&3\end{bmatrix}$
Now,
$\text{A}^\text{T}-\text{B}^\text{T}=\begin{bmatrix}3&4\\-1&2\\0&1\end{bmatrix}-\begin{bmatrix}-1&1\\2&2\\1&3\end{bmatrix}$
$=\begin{bmatrix}3+1&4-1\\-1-2&2-2\\0-1&1-3\end{bmatrix}$
$=\begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix}$
Therefore,
$\text{A}^\text{T}-\text{B}^\text{T}=\begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix}$

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