Question

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

Answer 1

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

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

By comparing the corresponding elements of the matrices

3a = a + 4

2a = 4 $\to$ a = 2

3b = 6 +a + b

2b – a = 6

2b -2 = 6

2b = 8 $\to$ b = 4

3d = 2d + 3

d = 3

3c = -1 +c + d

2c = -1 + d

2c = -1 +3 $\to$c = 1

Therefore a =2 , b = 4, c = 1, d = 3