Question

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

 

 

Answer 1

Given :

\[A^T = \begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 0 & 1\end{bmatrix} \text{and B} = \begin{bmatrix}- 1 & 2 & 1 \\ 1 & 2 & 3\end{bmatrix}\]

\[B^T = \begin{bmatrix}- 1 & 1 \\ 2 & 2 \\ 1 & 3\end{bmatrix}\]

Now,

\[A^T - B^T = \begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 0 & 1\end{bmatrix} - \begin{bmatrix}- 1 & 1 \\ 2 & 2 \\ 1 & 3\end{bmatrix}\] 

\[ = \begin{bmatrix}3 + 1 & 4 - 1 \\ - 1 - 2 & 2 - 2 \\ 0 - 1 & 1 - 3\end{bmatrix}\] 

\[ = \begin{bmatrix}4 & 3 \\ - 3 & 0 \\ - 1 & - 2\end{bmatrix}\]

Therefore

\[A^T - B^T = \begin{bmatrix}4 & 3 \\ - 3 & 0 \\ - 1 & - 2\end{bmatrix}\]