Solve the following questions.
If , find A – 1. Using A – 1, solve the system of linear equations:
x – 2y = 10, 2x + y + 3z = 8, – 2y + z = 7.
A =
|A| = 1(1 + 6) + 2(2 – 0) + 0
= 7 + 4
= 11
Now, the cofactors of A
C11 = (– 1)1 + 1 1 + 6 = 7
C21 = (– 1)2 + 1 – 2 – 0 = 2
C31 = (– 1)3 + 1 – 6 – 0 = – 6
C12 = (– 1)1 + 2 2 – 0 = – 2
C22 = (– 1)2 + 1 1 – 0 = 1
C32 = (– 1)3 + 1 3 – 0 = – 3
C13 = (– 1)1 + 2 – 4 – 0 = – 4
C23 = (– 1)2 + 1 – 2 – 0 = 2
C33 = (– 1)3 + 1 1 + 4 = 5
adj A =
A – 1 =
A – 1 =
Now the given equation can be written as:
A X B
Or, X = A – 1B
=
X =
X =
Hence, x = 4,y = – 3 and z = 1