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
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix}\)
Since \((B^T)^T = B\), the transpose of the given matrix (rows written as columns) is B:
\( B = \begin{bmatrix}-1&1\\2&2\\1&3\end{bmatrix} \)
Both A and B are of order \(3 \times 2\), so subtract corresponding entries:
\( A - B = \begin{bmatrix}3-(-1)&4-1\\-1-2&2-2\\0-1&1-3\end{bmatrix} \)
\( = \begin{bmatrix}4&3\\-3&0\\-1&-2\end{bmatrix} \)