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
Answer & explanation
Correct answer: option 2
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 $12$.