If \(\begin{bmatrix}5x + 8 & 7\\y + 3 & 10x + 12\end{bmatrix} = \begin{bmatrix}2 & 3y + 1\\5 & 0\end{bmatrix}\), then the value of \(5x + 3y\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
Equal matrices have equal corresponding entries:
\(5x + 8 = 2 \Rightarrow 5x = -6\)
\(y + 3 = 5 \Rightarrow y = 2\)
The other two entries agree: \(3y + 1 = 7\) and \(10x + 12 = 2(5x) + 12 = 0\). Hence
\(5x + 3y = -6 + 6 = 0\)