Q. 2 F3.5( 2 Votes )

# Solve the following system of equations by matrix method:3x + 4y + 2z = 82y – 3z = 3x – 2y + 6z = – 2

The given system can be written in matrix form as: or A X = B

A = , X = and B = Now, |A| = 3 = 3(12 – 6) – 4(0 + 3) + 2(0 – 2)

= 18 – 12 – 4

= 2

So, the above system has a unique solution, given by

X = A – 1B

Cofactors of A are:

C11 = (– 1)1 + 1 (12 – 6) = 6

C21 = (– 1)2 + 1(24 + 4) = – 28

C31 = (– 1)3 + 1(– 12 – 4) = – 16

C12 = (– 1)1 + 2 (0 + 3) = – 3

C22 = (– 1)2 + 1 18 – 2 = 16

C32 = (– 1)3 + 1 – 9 – 0 = 9

C13 = (– 1)1 + 2 (0 – 2) = – 2

C23 = (– 1)2 + 1 (– 6 – 4) = 10

C33 = (– 1)3 + 1 6 – 0 = 6

adj A = = A – 1 = Now, X = A – 1B = X = X = X = Hence, X = – 2,Y = 3 and Z = 1

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