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


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