If \(X+Y=\begin{bmatrix}2 & 1\\3 & 5\end{bmatrix}\) and \(X-Y=\begin{bmatrix}0 & 3\\7 & 9\end{bmatrix}\), then Y is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\begin{bmatrix}1 & -1\\-2 & -2\end{bmatrix}\)
Subtracting the second equation from the first removes X:
\( (X + Y) - (X - Y) = 2Y \)
\( \displaystyle 2Y = \begin{bmatrix}2 - 0 & 1 - 3\\3 - 7 & 5 - 9\end{bmatrix} = \begin{bmatrix}2 & -2\\-4 & -4\end{bmatrix} \)
\( \displaystyle Y = \begin{bmatrix}1 & -1\\-2 & -2\end{bmatrix} \)