Gauss Elimination Questions 1



In this page gauss elimination questions 1 we are going to see how to some examples in this method.

Question 1:

Find inverse of the following matrix using gauss elimination method

 
3 1 -1
2 -2 0
1 2 -1
 

Solution:

=

 
3 1 -1 1 0 0
2 -2 0 0 1 0
1 2 -1 0 0 1
 

R₃=> 2 R₃ - R

         2         4        -2        0         0        2       

         2        -2        0         0         1        0

         (-)      (+)      (-)        (-)         (-)      (-) 

      _______________________________________

       0        6        -2        0        -1        2

      ________________________________________

=

 
3 1 -1 1 0 0
2 -2 0 0 1 0
0 6 -2 0 -1 2
 

R => 3R₂ - 2R₁

       6         -6          0        0         3        0       

         6          2         -2        2         0        0

        (-)       (-)       (+)         (-)       (-)      (-) 

      _________________________________________

       0        -8         2       -2        3        0

      _______________________________________

=

 
3 1 -1 1 0 0
0 -8 2 -2 3 0
0 6 -2 0 -1 2
 

R₃ => 8R₃ + 6R

         0        48        -16          0        -8         16       

         0       -48         12        -12        18        0

      ______________________________________

       0         0        -4         -12        10        16

      _____________________________________

=

 
3 1 -1 1 0 0
0 -8 2 -2 3 0
0 0 -4 -12 10 16
 

R₁ => 8R₁ + R

        24       8        -8        8        0         0      

         0       -8         2        -2        3        0

      _________________________________

       24       0        -6        6       3        0

      __________________________________

=

 
24 0 -6 6 3 0
0 -8 2 -2 3 0
0 0 -4 -12 10 16
 

R₁ => 4R -  6R

         96       0       -24       24      12        0        

         0        0       -24      -72      60        96

        (-)       (-)     (+)      (+)       (-)      (-)

      ________________________________________

       96       0        0       96       -48     -96

      ________________________________________

=

 
96 0 0 96 -48 -96
0 -8 2 -2 3 0
0 0 -4 -12 10 16
 

R => 2 R + R

        0       -16       4       -4       6         0        

         0        0       -4      -12      10      16

      ________________________________

       0       -16        0      -16      16     16

      _________________________________

=

 
96 0 0 96 -48 -96
0 -16 0 -16 16 16
0 0 -4 -12 10 16
 

R÷ 96    R÷(- 16)       R₃  ÷ (-4)

=

 
1 0 0 1 -1/2 -1
0 1 0 1 -1 -1
0 0 1 3 -5/2 -4
 

Inverse of the given matrix =

gauss elimination question1gauss elimination questions 1

 
1 -1/2 -1
1 -1 -1
3 -5/2 -4
 

Questions



Solution


2) Find the inverse of the following matrix using gauss elimination method

 
2 1 1
1 1 1
1 -1 0
 

Solution

3) Find the inverse of the following matrix using gauss elimination method

 
1 2 1
2 -1 2
1 1 -2
 

Solution

4) Find the inverse of the following matrix using gauss elimination method

 
6 2 3
3 1 1
10 3 4
 

Solution

5) Find the inverse of the following matrix using gauss elimination method

 
2 5 7
1 1 1
2 1 -1
 

Solution

6) Find the inverse of the following matrix using gauss elimination method

 
3 1 -1
2 -1 2
2 1 -2
 

gauss elimination questions 1 gauss elimination questions 1

Solution






Gauss Elimination Question1 to Inverse of a matrix
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