Given as 2y – z = 1
x – y + z = 2
2x – y = 0
The given equation can be written in matrix form
= 0 + 4 – 1
= 3
So, the above system has a unique solution, given by
X = A – 1B
Co-factors 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
So, X = 1, Y = 1 and Z = 1.
