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find the invers matrix [1 2 1 2 -1 -1 3 1 1]

find the invers matrix


[1  2  1


 2 -1   -1


 3  1   1]


 

Grade:12

2 Answers

mahesh dasari
31 Points
11 years ago

if given equation is  AX = B form then for finding X

we write it like  [ A : B] = X

so for finding inverse

AA-1 = I

[A : I ] = A-1

I think u may know about row reduction

Applying the method of Gauss-Jordon
elimination, we get inverse of matrix

?? : ??3 =

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

apply row reduction

R2 - 2R1 , R3 - 3R1 ,

 1  
 2  
 1  
 1 
 0  
 0 
 0
  -5
  -3
  -2 
 1
  0
 0
  -5
  -2
  -3
  0
  1

- R2 / 5

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

R1 - 2R2

R3 + 5R2

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

R1 + R3/5

R2 - 3R3/5

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

This is combination of two 3X3 matrices first matrix is Identity matrix  and second matrix is A-1 matrix

for finding A-1 we always reduce the first matrix into indentity matrix and second is A-1

So A-1 =

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

like this you can find A-1

Another process is there to find A-1 is

A-1 = adjoint(A) / det( A)

above process is very easy than this

ok thank u , if u like support my answer

srinu kummari
32 Points
11 years ago

invers matrix is that [1 2 3

                                     2 -1 1

                                       1 -1 1]

 

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