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

11

The correct answer is Option (2) → 11 **

$\begin{pmatrix}x-y & t\\ 2x-y & w\end{pmatrix} =\begin{pmatrix}-1 & 2\\ 0 & 1\end{pmatrix}$

$x-y=-1,\quad t=2$

$2x-y=0,\quad w=1$

Subtracting the first two equations:

$(2x-y)-(x-y)=0-(-1)$

$x=1$

$x-y=-1\;\Rightarrow\;1-y=-1\;\Rightarrow\;y=2$

Now evaluate:

$2x+y+3t+w=2(1)+2+3(2)+1$

$=2+2+6+1$

$=11$

The required value is $11$.