Q. 2 D4.3( 3 Votes )

# Solve the following system of equations by matrix method:

3x + 4y + 7z = 14

2x – y + 3z = 4

X + 2y – 3z = 0

Answer :

The given system can be written in matrix form as:

or A X = B

A = , X = and B =

Now, |A| = 3

= 3(3 – 6) – 4(– 6 – 3) + 7(4 + 1)

= – 9 + 36 + 35

= 62

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

X = A ^{– 1}B

Cofactors of A are:

**C _{11}** = (– 1)

^{1 + 1}3 – 6 = – 3

**C _{21}** = (– 1)

^{2 + 1}– 12 – 14 = 26

**C _{31}** = (– 1)

^{3 + 1}12 + 7 = 19

**C _{12}** = (– 1)

^{1 + 2}– 6 – 3 = 9

**C _{22}** = (– 1)

^{2 + 1}– 3 – 7 = – 10

**C _{32}** = (– 1)

^{3 + 1}9 – 14 = 5

**C _{13}** = (– 1)

^{1 + 2}4 + 1 = 5

**C _{23}** = (– 1)

^{2 + 1}6 – 4 = – 2

**C _{33}** = (– 1)

^{3 + 1}– 3 – 8 = – 11

adj A =

=

A ^{– 1} =

Now, X = A ^{– 1}B =

X =

X =

X =

Hence, X = 1,Y = 1 and Z = 1

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