If $\begin{bmatrix}2a+b&a-2b\\5c-d&4c+3d\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix}$, then the value of $a + 2b - 3c + 4d$ is equal to

12

The correct answer is Option (2) → 12

Given

$2a+b=4$

$a-2b=-3$

$5c-d=11$

$4c+3d=24$

From $a-2b=-3$

$a=-3+2b$

Substitute in $2a+b=4$

$2(-3+2b)+b=4$

$-6+4b+b=4$

$5b=10$

$b=2$

$a=-3+2(2)=1$

From $5c-d=11$

$d=5c-11$

Substitute in $4c+3d=24$

$4c+3(5c-11)=24$

$4c+15c-33=24$

$19c=57$

$c=3$

$d=5(3)-11=4$

Now

$a+2b-3c+4d=1+2(2)-3(3)+4(4)$

$=1+4-9+16$

$=12$

The value of $a+2b-3c+4d$ is $12$.