The value of $a+b+c+d$ if $\left[\begin{array}{ll}2 a+b & a+2 b \\ 2 c+d & c+2 d\end{array}\right]=\left[\begin{array}{ll}8 & 4 \\ 3 & 3\end{array}\right]$ is :

6

$\left[\begin{array}{cc}2 a+b & a+2 b \\ 2 c+d & c+2 d\end{array}\right]=\left[\begin{array}{ll}8 & 4 \\ 3 & 3\end{array}\right]$

⇒ 2a + b = 8  .....(1)

a + 2b = 4  .....(2)

2c + d = 3  .....(3)

c + 2d = 3   .....(4)

adding (1), (2), (3), (4)

3a + 3b + 3c + 3d = 18

3(a + b + c + d) = 18

a + b + c + d = 6