Solve the following system of equations by matrix method:
8x + 4y + 3z = 18
2x + y + z = 5
X + 2y + z = 5
The given system can be written in matrix form as:
AX = B
Now, |A| = 8
= 8(– 1) – 4(1) + 3(3)
= – 8 – 4 + 9
= – 3
So, the above system has a unique solution, given by
X = A – 1B
Cofactors of A are:
C11 = (– 1)1 + 1 1 – 2 = – 1
C21 = (– 1)2 + 1 4 – 6 = 2
C31 = (– 1)3 + 1 4 – 3 = 1
C12 = (– 1)1 + 2 2 – 1 = – 1
C22 = (– 1)2 + 1 8 – 3 = 5
C32 = (– 1)3 + 1 8 – 6 = – 2
C13 = (– 1)1 + 2 4 – 1 = 3
C23 = (– 1)2 + 1 16 – 4 = – 12
C33 = (– 1)3 + 1 8 – 8 = 0
adj A =
=
A – 1 =
Now, X = A – 1B =
X =
X =
X =
Hence, X = 1,Y = 1 and Z = 2