If \(A = \begin{bmatrix}2&-1\\0&3\\4&1\end{bmatrix}\) and \(B = \begin{bmatrix}1&2&0\\-3&1&5\end{bmatrix}\), then \(A' + B\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\begin{bmatrix}3&2&4\\-4&4&6\end{bmatrix}\)
The transpose \(A'\) is obtained by writing the rows of A as columns. A is of order \(3 \times 2\), so \(A'\) is of order \(2 \times 3\), the same as B.
\( \displaystyle A' = \begin{bmatrix}2&0&4\\-1&3&1\end{bmatrix} \)
Adding corresponding elements:
\( \displaystyle A' + B = \begin{bmatrix}2 + 1&0 + 2&4 + 0\\-1 - 3&3 + 1&1 + 5\end{bmatrix} \)
\( \displaystyle = \begin{bmatrix}3&2&4\\-4&4&6\end{bmatrix} \)