For two matrices $A =\begin{bmatrix}3&4\\-1&2\\0&1\end{bmatrix}$ and $B^T =\begin{bmatrix}-1&2&1\\1&2&3\end{bmatrix}$, $A - B$ equals

$\begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix}$

The correct answer is Option (4) → $\begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix}$

Given matrices:

$A = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$

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

Transpose $B^T$ to get $B$:

$B = \begin{bmatrix} -1 & 1 \\ 2 & 2 \\ 1 & 3 \end{bmatrix}$

Check dimensions: $A$ is $3 \times 2$, $B$ is $3 \times 2$ → subtraction possible

$A - B = \begin{bmatrix} 3 - (-1) & 4 - 1 \\ -1 - 2 & 2 - 2 \\ 0 - 1 & 1 - 3 \end{bmatrix} = \begin{bmatrix} 4 & 3 \\ -3 & 0 \\ -1 & -2 \end{bmatrix}$