Q. 2 F3.5( 2 Votes )

# Solve the following system of equations by matrix method:

3x + 4y + 2z = 8

2y – 3z = 3

x – 2y + 6z = – 2

Answer :

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 ^{– 1}B

Cofactors of A are:

**C _{11}** = (– 1)

^{1 + 1}(12 – 6) = 6

**C _{21}** = (– 1)

^{2 + 1}(24 + 4) = – 28

**C _{31}** = (– 1)

^{3 + 1}(– 12 – 4) = – 16

**C _{12}** = (– 1)

^{1 + 2}(0 + 3) = – 3

**C _{22}** = (– 1)

^{2 + 1}18 – 2 = 16

**C _{32}** = (– 1)

^{3 + 1}– 9 – 0 = 9

**C _{13}** = (– 1)

^{1 + 2}(0 – 2) = – 2

**C _{23}** = (– 1)

^{2 + 1}(– 6 – 4) = 10

**C _{33}** = (– 1)

^{3 + 1}6 – 0 = 6

adj A =

=

A ^{– 1} =

Now, X = A ^{– 1}B =

X =

X =

X =

Hence, X = – 2,Y = 3 and Z = 1

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