If \(2\begin{bmatrix}x&5\\7&y - 3\end{bmatrix} + \begin{bmatrix}3&-4\\1&2\end{bmatrix} = \begin{bmatrix}7&6\\15&14\end{bmatrix}\), then the value of \(x + y\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 11
In scalar multiplication every element is multiplied by the scalar, and matrices are added element by element:
\( \displaystyle 2\begin{bmatrix}x&5\\7&y - 3\end{bmatrix} + \begin{bmatrix}3&-4\\1&2\end{bmatrix} = \begin{bmatrix}2x + 3&6\\15&2y - 4\end{bmatrix} \)
By equality of matrices:
\(2x + 3 = 7\)
\(x = 2\)
\(2y - 4 = 14\)
\(y = 9\)
Hence
\(x + y = 2 + 9 = 11\)