If $\left[\begin{array}{cc}b & 2 b-c \\ d-3 c & 5 a-d\end{array}\right]=\left[\begin{array}{cc}4 & 7 \\ 5 & 12\end{array}\right]$, then the values of a, b, c, d are

a = 4, b = 4, c = 1, d = 8

The correct answer is Option (2) → a = 4, b = 4, c = 1, d = 8

$\begin{bmatrix} b & 2b - c \\ d - 3c & 5a - d \end{bmatrix} = \begin{bmatrix} 4 & 7 \\ 5 & 12 \end{bmatrix}$

$b = 4$

$2b - c = 7 \Rightarrow 8 - c = 7 \Rightarrow c = 1$

$d - 3c = 5 \Rightarrow d - 3 = 5 \Rightarrow d = 8$

$5a - d = 12 \Rightarrow 5a - 8 = 12 \Rightarrow 5a = 20 \Rightarrow a = 4$

$a = 4,\ b = 4,\ c = 1,\ d = 8$