If \(\begin{bmatrix}2^x&-1\\0&3^y\end{bmatrix} = \begin{bmatrix}16&-1\\0&27\end{bmatrix}\), then the value of \(x + y\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7
Two matrices are equal when their corresponding elements are equal. Comparing the diagonal elements:
\(2^x = 16 = 2^4\), so \(x = 4\)
\(3^y = 27 = 3^3\), so \(y = 3\)
Hence
\(x + y = 4 + 3 = 7\)