Find the values of $a,b,c$ and $d$, if
$3\left[ {\begin{array}{llllllllllllllllllll}a&b\\c&d\end{array}} \right] = \left[ \begin{array}{l}a\,\,\,\,\,\,\,\,\,\,6\\ - 1\,\,\,\,\,\,\,2d\end{array} \right] + \left[ {\begin{array}{cccccccccccccccccccc}4&{a + b}\\{c + d}&3\end{array}} \right]z$.

We have,
$3\left[ {\begin{array}{llllllllllllllllllll}a&b\\c&d\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}a&6\\{ - 1}&{2d}\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}4&{a + b}\\{c + d}&3\end{array}} \right]$

$\Rightarrow$ $\left[ {\begin{array}{llllllllllllllllllll}{3a}&{3b}\\{3c}&{3d}\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}{a + 4}&{6 + a + b}\\{c + d - 1}&{3 + 2d}\end{array}} \right]$

$\Rightarrow$ $3a = a + 4 \Rightarrow a = 2$;
$3b = 6 + a + b$

$\Rightarrow$ $3b - b = 8 \Rightarrow b = 4$;

$3d = 3 + 2d \Rightarrow d = 3$
and $\Rightarrow$ $3c = c + d - 1$

$\Rightarrow$ $2c = 3 - 1c = 1$
$\therefore$ $a = 2,b = 4,c = 1$ and $d = 3$