Q8 of 75 Page 8

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


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