Question

If possible, using elementary row transformations, find the inverse of the following matrices

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

Answer 1

Here, A = `[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`

Put A = IA

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

R₁ → R₁ – 2R₃ and R₂ → R₂ + R₁

`[(0, 1, -1),(0, -1, 1),(1, 1, -1)] = [(1, 0, -2),(0, 1, 1),(0, 0, 1)]"A"`

R₁ → R₁ + R₂ 

`[(0, 0, 0),(0, -1, 1),(1, 1, -1)] = [(1, 1, -1),(0, 1, 1),(0, 0, 1)]"A"`

First row on L.H.S. contains all zeros

So the inverse of the given matrix A does not exist.

Hence, matrix A has no inverse.