Find the values of $a, b, c$ and $d$, if $3 \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix} + \begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}$.

$a = 2, b = 4, c = 1, d = 3$

The correct answer is Option (2) → $a = 2, b = 4, c = 1, d = 3$ ##

We have,

$3 \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix} + \begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}$

$\Rightarrow \begin{bmatrix} 3a & 3b \\ 3c & 3d \end{bmatrix} = \begin{bmatrix} a+4 & 6+a+b \\ c+d-1 & 3+2d \end{bmatrix}$

On comparing the corresponding elements of both sides, we get

$\Rightarrow 3a = a + 4 \Rightarrow a = 2;$

$3b = 6 + a + b$

$\Rightarrow 3b - b = 6 + 2 \Rightarrow 2b = 8 \Rightarrow b = 4; \quad [∵a = 2]$

$3d = 3 + 2d \Rightarrow d = 3$

and $3c = c + d - 1$

$\Rightarrow 2c = 3 - 1 \Rightarrow c = 1 \quad [∵d = 3]$

$∴a = 2, b = 4, c = 1 \text{ and } d = 3$