Question

Apply the given elementary transformation of the following matrix.

Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.

Answer 1

convert `[(1,-1),(2,3)]` into identify matrix by suitable row motion

∴ AA⁻¹ = I

A⁻¹ `[(1,-1),(2,3)]=[(1,0),(0,1)]`

Applying Elementary Row operation.

R₁ → R₁ + `1/3`R₂

A6−1 `[(5/3,0),(2,3)]=[(1,1/3),(0,1)]`

R₁ → `3/5` R₁

A⁻¹ `[(1,0),(2,3)]=[(3/5,1/5),(0,1)]`

A₁ `[(1,0),(0,3)]=[(3/5,1/5),((-6)/5,3/5)]`

R₂ → `1/3` R₂

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

So, A⁻¹ `[(3/5,1/5),((-2)/5,1/5)]`