Gauss Elimination Questions 2



In this page gauss elimination questions 2 we are going to see solution of third question in the worksheet of gauss elimination method.

Question 2:

Find inverse of the following matrix using gauss elimination method

 
2 1 1
1 1 1
1 -1 0
 

Solution:

=

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

R₃=> R₃ - R

         1       -1        2        0          0        1       

         1        1        1         0         1        0

         (-)      (-)     (-)       (-)       (-)      (-) 

      ________________________________________

       0        -2        1        0        -1        1

      ________________________________________

=

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

R => 2R₂ - R₁

          2       2        2          0        2        0       

         2        1        1         1        0        0

         (-)      (-)       (-)        (-)       (-)      (-) 

      ________________________________________

       0       1        1        -1        2        0

      _________________________________________

=

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

R₃ =>R₃ + 2R

       0      -2       1         0        -1        1       

         0        2       2        -2        4        0

      ________________________________________

       0       0        3        -2        3        1

      _______________________________________

=

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

R₁ => R₁ - R

         2       1        1          1        0        0       

         0       1        1         -1        2        0

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

      ________________________________________

       2       0        0        2        2        0

      ________________________________________

=

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

R => 3R₂ - R

        0       3        3         -3        6        0       

         0       0        3         -2        3        1

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

      _________________________________________

       0       3        0        -1        3        -1

      ______________________________________

=

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

gauss elimination question2 gauss elimination question2

R÷ 2           R, R₃  ÷ 3

=

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

Inverse of the given matrix =

 
1 1 0
-1/3 1 -1/3
-2/3 1 1/3
 

Questions



Solution


1) 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 2 gauss elimination questions 2 gauss elimination questions 2

Solution






Gauss Elimination Question2 to Inverse of a matrix
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