If \(\begin{bmatrix}2x+y & 4x\\ 5x-7 & 4x\end{bmatrix}=\begin{bmatrix}7 & 7y-13\\ y & x+6\end{bmatrix}\), then \(4x+5y\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 23
Two matrices are equal when their corresponding entries are equal. The (2, 2) entries give x at once:
\(4x = x+6\)
\(x = 2\)
The (2, 1) entries then give y:
\(5x-7 = y\)
\(y = 10-7 = 3\)
Check with the other entries: \(2x+y = 4+3 = 7\) and \(7y-13 = 21-13 = 8 = 4x\).
\(4x+5y = 8+15 = 23\)