Question

If A = `[(1,2),(3,4)]` and AX = I then find X by using elementary transformations

Answer 1

We have, AX = I

∴ `[(1,2),(3,4)]X = [(1,0),(0,1)]`

Applying R₂ → R₂ − 3R₁

`[(0,1),(0,-2)]X = [(1,0),(-3,1)]`

Applying `R_2 →(-1/2) R_2`

`[(1,2),(0,1)]X = [(1,0),(3/2 , -1/2)]`

Applying R₁ → R₁ − 2R₂

`[(1,0),(0,1)]X = [(-2,1),(3/2, -1/2)]`

∴ `X = [(-2,1),(3/2, -1/2)]`