## Inversion Method Questions 5

In this page inversion method questions 5 we are going to see how to solve the given linear equations using this particular method in matrices.

Question 5:

Solve the following linear equation by inversion method

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2

Solution:

First we have to write the given equation in the form AX = B. Here X represents the unknown variables. A represent coefficient of the variables and B represents constants.

 3 1 -1 2 -1 2 2 1 -2

 x y z

=

 2 6 -2

To solve this we have to apply the formula X = A⁻¹ B

|A|

=

 3 1 -1 2 -1 2 2 1 -2

|A|

= 3

 -1 2 1 -2

- 1

 2 2 2 -2

-1

 2 -1 2 1

|A| = 3 [2-2] - 1 [-4-4] - 1 [2-(-2)]

= 3 [0] - 1 [-8] -1 [2+2]

= 3 [0] - 1 [-8] -1 [4]

= 0 + 8 - 4

= 4

|A| = 4 ≠ 0

Since A is a non singular matrix. A⁻¹ exists.inversion method questions 5

minor of 4

=
 -1 2 1 -2

= [2-2]

= 0

Cofactor of 4

=  + (0)

=    0

minor of 1

=
 2 2 2 -2

= [-4-4]

= (-8)

= -8

Cofactor of 1

=  - (-8)

=    8

minor of -1

=
 2 -1 2 1

nversion method questions 5

= [2-(-2)]

= (2+2)

= 4

Cofactor of -1

=  + (4)

=    4

minor of 2

=
 1 -1 1 -2

= [-2-(-1)]

= (-2+1)

= -1

= -1

Cofactor of 2

=  - (-1)

=    1

minor of -1

=
 3 -1 2 -2

= [-6-(-2)]

= (-6+2)

= -4

= -4

Cofactor of -1

=  + (-4)

=    -4

minor of 2

=
 3 1 2 1

= [3-2]

= 1

Cofactor of 2

=  - (1)

=    -1

minor of 2

=
 1 -1 -1 2

= [2-1]

= 1

Cofactor of 2

=  + (1)

=    1

minor of 1

=
 3 -1 2 2

= [6-(-2)]

= [6+2]

= 8

Cofactor of 1

=  - (8)

=    -8

minor of -2

=
 3 1 2 -1

inversion method questions 5

= [-3-2]

= [-5]

= -5

Cofactor of -2

=  + (-5)

=    -5

co-factor matrix =

 0 8 4 1 -4 -1 5 0 -5

adjoint of matrix=

 0 1 5 8 -4 0 4 -1 -5

A⁻¹ = 1/4

 0 1 5 8 -4 0 4 -1 -5

 x y z

= 1/4

 0 1 5 8 -4 0 4 -1 -5

 2 6 -2

= 1/4

 0 1 5

x

 2 6 -2

 8 -4 0

x

 2 6 -2

 4 -1 -5

x

 2 6 -2

 x y z

=1/4

 (0+6-10) (16-24+0) (8-6+10)

=1/4

 (-4) (-8) (12)

 x y z

=

 -1 -2 3

Solution:

x = -1

y = -2

z = 3          inversion method questions 5  inversion method questions 5

Inversion Method Question5 to Inversion Method
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