Solve the following questions.
If , find A – 1. Using A – 1, solve the system of linear equations
x – 2y = 10, 2x – y – z = 8, – 2y + z = 7.
A =
|A| = 1(– 1 – 1) – 2(– 2 – 0) + 0
= – 2 + 4
= 2
Now, the cofactors of A
C11 = (– 1)1 + 1 – 1 – 1 = – 2
C21 = (– 1)2 + 1 2 – 0 = 2
C31 = (– 1)3 + 1 – 2 – 0 = – 2
C12 = (– 1)1 + 2 2 – 0 = – 2
C22 = (– 1)2 + 1 1 – 0 = 1
C32 = (– 1)3 + 1 – 1 – 0 = 1
C13 = (– 1)1 + 2 – 2 – 0 = – 2
C23 = (– 1)2 + 1 – 1 – 0 = 1
C33 = (– 1)3 + 1 – 1 + 4 = 3
adj A =
A – 1 =
A – 1 =
Now the given equation can be written as:
A X B
Or, X = A – 1B
=
X =
Hence, x = – 3,y = 2.5 and z = – 4.5