# 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)]

#### 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
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