If \(A = \begin{bmatrix}1&3\\-2&4\end{bmatrix}\), \(B = \begin{bmatrix}5&-1\\0&6\end{bmatrix}\) and \(2X + A = B\), then the matrix X is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\begin{bmatrix}2&-2\\1&1\end{bmatrix}\)
Matrix addition and scalar multiplication work element by element, so the equation can be solved like an ordinary equation:
\(2X = B - A\)
\( \displaystyle B - A = \begin{bmatrix}5 - 1&-1 - 3\\0 + 2&6 - 4\end{bmatrix} = \begin{bmatrix}4&-4\\2&2\end{bmatrix} \)
\( \displaystyle X = \frac{1}{2}\begin{bmatrix}4&-4\\2&2\end{bmatrix} = \begin{bmatrix}2&-2\\1&1\end{bmatrix} \)