Question:
Find the value of a, b, c and d, if
Solution:
Given,
$3\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{cc}a & 6 \\ -1 & 2 d\end{array}\right]+\left[\begin{array}{cc}4 & a+b \\ c+d & 3\end{array}\right]$
$\left[\begin{array}{ll}3 a & 3 b \\ 3 c & 3 d\end{array}\right]=\left[\begin{array}{cc}a+4 & 6+a+b \\ -1+c+d & 2 d+3\end{array}\right]$
Now,
3a = a + 4 ⇒ a = 2
3b = 6 + a + b
3b – b = 8
⇒ b = 4
And,
3d = 3 + 2d
⇒ d = 3
And,
3c = c + d – 1
2c = 3 – 1 = 2
⇒ c = 1
Hence,
a = 2, b = 4, c = 1 and d = 3
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