Given as 2x + y + z = 2
x + 3y – z = 5
3x + y – 2z = 6
The given equation can be written in matrix form
= 2(– 6 + 1) – 1(– 2 + 3) + 1(1 – 9)
= – 10 – 1 – 8
= – 19
So, the above system has a unique solution, given by
X = A – 1B
Co-factors of A are
C11 = (– 1)1 + 1 – 6 + 1 = – 5
C21 = (– 1)2 + 1(24 + 4) = – 28
C31 = (– 1)3 + 1 – 1 – 3 = – 4
C12 = (– 1)1 + 2 – 2 + 3 = – 1
C22 = (– 1)2 + 1 – 4 – 3 = – 7
C32 = (– 1)3 + 1 – 2 – 1 = 3
C13 = (– 1)1 + 21 – 9 = – 8
C23 = (– 1)2 + 12 – 3 = – 1
C33 = (– 1)3 + 1 6 – 1 = 5
So, X = 1, Y = 1 and Z = -1
