GAUSS ELIMINATION QUESTION1

About "Gauss elimination question1"

Gauss elimination question1 :

we are going to see 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 => 4R₂ -  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 R₂ + 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 =

 
1 -1/2 -1
1 -1 -1
3 -5/2 -4
 

Gauss elimination - Practice questions

2) Find the inverse of the following matrix using gauss elimination method Gauss elimination question1

 
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
 

Solution

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