Solution:

As, $\left[ \begin{matrix} a+c & a+2b \\ c-1 & 4d-6 \\ \end{matrix} \right]$ = $\left[ \begin{matrix} 0 & -7 \\ 3 & 2d \\ \end{matrix} \right]$

 

By comparing the corresponding elements, we get

$a + c = 0$

$a = -c$ ---------------(i)

 

$a + 2b = -7$

$2b = - (a+7)$ ---------------(ii)

 

$c - 1 = 3$

$c = 3 + 1$

$c = 4$ ---------------(iii)

 

By putting the value of “c” in equation (i), we will get

$a = -4$ ---------------(iv)

 

By putting the value of “a” in equation (ii), we will get

$2b = - (-4+7)$

$2b = - (3)$

$b = -{\large \frac{3}{2}} $

$b = - 1.5$ ---------------(v)

 

Similarly,

$4d - 6 = 2d$

$4d - 2d = 6$

$2d = 6$

$d =-{\large \frac{6}{2}}$

$d = 3$ ---------------(vi)

 

From equations (iii), (iv), (v) and (vi) we get

$a = - 4$, $b = - 1.5$, $c = 4$ and $d = 3$