If \(\begin{bmatrix}x - y & t\\2x - y & w\end{bmatrix} = \begin{bmatrix}-1 & 2\\0 & 1\end{bmatrix}\), then \(2x + y + 3t + w\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 11
Equal matrices have equal corresponding entries:
\(x - y = -1,\quad t = 2\)
\(2x - y = 0,\quad w = 1\)
Subtracting the first equation from the second:
\(x = 1\)
\(y = x + 1 = 2\)
\(2x + y + 3t + w = 2 + 2 + 6 + 1 = 11\)