Question

Find the values of a,b,c and d from the equation $\left[\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right]=\left[\begin{array}{cc}-5& 5\\ 0& 13\end{array}\right].$

Answer 1

Given,$\left[\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right]=\left[\begin{array}{cc}-5& 5\\ 0& 13\end{array}\right].$
By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
a-b=-5 ...(i)
2a-b=0...(ii)
2a+c=5....(iii)
and 3c+d=13 ....(iv)
Subtracting Eq.(i)from Eq.(ii), we get a = 5
Putting a = 5 in Eq. (i)and Eq. (iii), we get
5-b=-5 and 2(5)+c=5
$\Rightarrow b=10$ and c=-5
Substituting c=-5 in Eq. (iv), we obtain
$3\times -5+d=13\Rightarrow d=13+15=28$
Hence, a=5, b=10, c=-5 and d=28.