Advertisement Remove all ads

Using elementary row transformation, find the inverse of the matrix(2,-3,5),(3,2,-4),(1,1,-2) - Mathematics

Sum

Using elementary row transformation, find the inverse of the matrix

`[(2,-3,5),(3,2,-4),(1,1,-2)]`

Advertisement Remove all ads

Solution

We have A =`[(2,-3,5),(3,2,-4),(1,1,-2)]`

A=IA `[(2,-3,5),(3,2,-4),(1,1,-2)]=[(1,0,0),(0,1,0),(1,0,0)]`A

R1 ↔ R3

`[(1,1,-2),(3,2,-4),(2,-3,5)]=[(0,0,1),(0,1,0),(1,0,0)]`A

R2 → R2 - 3R1,
R3 → R3 - 2R1

`[(1,1,-2),(0,-1,2),(0,-5,9)]=[(0,0,1),(0,1,-3),(1,0,-2)]`A

R2 → R1 +R2 ,
R3 → R3 - 5R2

`[(1,0,0),(0,-1,2),(0,0,-1)]=[(0,0,-2),(0,1,-3),(1,-5,13)]`A

R2 → - R2 ,
R3 → - R3

`[(1,0,0),(0,1,-2),(0,0,1)]=[(0,1,-2),(0,-1,3),(-1,5,-13)]`A

R2 → R2 + 2R3

`[(1,0,0),(0,1,0),(0,0,1)]=[(0,1,-2),(-2,9,-23),(-1,5,-13)]`A

We know, I = AA-1 

Therefore, inverse of A i.e. `"A"^-1 = [(0,1,-2),(-2,9,-23),(-1,5,-13)]`

Concept: Inverse of a Matrix - Inverse of a Nonsingular Matrix by Elementary Transformation
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×