Solve the following system of equations by matrix method:

2y – z = 1


x – y + z = 2


2x – y = 0

The given system can be written in matrix form as:



AX = B


Now, |A| = 0


= 0 + 4 – 1


= 3


So, the above system has a unique solution, given by


X = A – 1B


Cofactors of A are:


C11 = (– 1)1 + 1 1 – 0 = 1


C21 = (– 1)2 + 11 – 2 = 1


C31 = (– 1)3 + 10 + 1 = 1


C12 = (– 1)1 + 2 – 2 – 0 = 2


C22 = (– 1)2 + 1 – 1 – 0 = – 1


C32 = (– 1)3 + 1 0 – 2 = 2


C13 = (– 1)1 + 2 4 – 0 = 4


C23 = (– 1)2 + 1 2 – 0 = – 2


C33 = (– 1)3 + 1 – 1 + 2 = 1


adj A =


=


A – 1 =


Now, X = A – 1B =


X =


X =


X =


Hence, X = 1,Y = 2 and Z = 3


2