Inversion Method Questions 4





In this page inversion method questions 4 we are going to see how to solve the given linear equations using this particular method in matrices.

Question 4:

Solve the following linear equation by inversion method

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0

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.



 
2 5 7
1 1 1
2 1 -1
 
 
x
y
z
 
 
=
 
52
9
0
 
 

|A|

 = 2

 
1 1

1 -1
 

-5

 
1 1

2 -1
 

+7

 
1 1

2 1
 

|A| = 2 [-1-1] - 5 [-1-2] + 7 [1-2]

      = 2 [-2] - 5 [-3] + 7 [-1]

      = -4 + 15 - 7

      = -11 + 15

      = 4

|A| = 4 ≠ 0

Since A is a non singular matrix. A⁻¹ exists.inversion method questions 4

minor of 2

=
1 1
1 -1

inversion method questions 4

   = [-1-1]

   = (-2)

   = -2

Cofactor of 2

   =  + (-2)

   =    -2

minor of 5

=
1 1
2 -1

   = [-1-2]

   = -3

Cofactor of 5

   =  - (-3)

   =    3

minor of 7

=
1 1
2 1

   = [1-2]

   = -1

Cofactor of 7

   =  + (-1)

   =    -1

minor of 1

=
5 7
1 -1

   = [-5-7]

   = -12

Cofactor of 1

   =  - (-12)

   =    12

minor of 1

=
2 7
2 -1

   = [-2-14]

   = -16

Cofactor of 1

   =  + (-16)

   =   -16

minor of 1

=
2 5
2 1

   = [2-10]

   = -8

Cofactor of 1

   =  - (-8)

   =   8

minor of 2

=
5 7
1 1

   = [5-7]

   = -2

Cofactor of 2

   =  + (-2)

   =   -2

minor of 1

=
2 7
1 1

   = [2-7]

   = -5

Cofactor of 1

   =  - (-5)

   =   5

minor of -1

=
2 5
1 1

inversion method questions 4

   = [2-5]

   = -3

Cofactor of -1

   =  + (-3)

   =   -3

co-factor matrix =

 
-2 3 -1
12 -16 8
-2 5 -3
 

adjoint of matrix=

 
-2 12 -2
3 -16 5
-1 8 -3
 

          A⁻¹ = 1/4

 
-2 12 -2
3 -16 5
-1 8 -3
 
 
x
y
z
 
 

  = 1/4

 
-2 12 -2
3 -16 5
-1 8 -3
 
 
52
9
0
 
 


  = 1/4


 
-2 12 -2
 
x
 
52
9
0
 
 
3 -16 5
 
x
 
52
9
0
 
 
-1 8 -3
 
x
 
52
9
0
 
 
x
y
z
 
 

=1/4

 
(-104+108+0)
(156-144+0)
(-52+72+0)
 
 

=1/4

 
(4)
(12)
(20)
 
 
 
x
y
z
 
 
 
1
3
5
 
 

Solution:

x = 1

y = 3

z = 5







Inversion Method Question4 to Inversion Method
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