If $\begin{bmatrix}a+2 & 3b+2c\\c+3&7d+6\end{bmatrix}=\begin{bmatrix}2 & -3\\3c& -8\end{bmatrix},$ then the values of a, b, c and d are,

$a=0, b=-2, c=\frac{3}{2}, d=-2$

The correct answer is Option (4) → $a=0, b=-2, c=\frac{3}{2}, d=-2$

$\begin{bmatrix}a+2 & 3b+2c\\c+3&7d+6\end{bmatrix}=\begin{bmatrix}2 & -3\\3c& -8\end{bmatrix}$

$⇒a+2=2$

$⇒a=0$

and, $⇒7d+6=-8$

$⇒7d=-14$

$⇒d=-2$

and, $⇒c+3=3c$

$⇒3=2c$

$⇒c=\frac{3}{2}$

and, $3b+2c=-3$

$⇒3b+3=-3$

$⇒3b=-3-3=-6$

$⇒b=-2$