Question

Find inverse of the following matrices (if they exist) by elementary transformations:

`[(2, 1),(7, 4)]`

Answer 1

Let A = `[(2, 1),(7, 4)]`

∴ |A| = `|(2, 1),(7, 4)|`

= 8 – 7
= 1 ≠ 0
∴ A^–1 exists.
Consider AA^–1 = I

∴ `[(2, 1),(7, 4)] A^-1 = [(1, 0),(0, 1)]`

Applying R₁ → `(1/2)`R₁, we get

`[(1, 0.5),(7, 4)] A^-1 = [(0.5, 0),(0, 1)]`

Applying R₂ → R₂ – 7R₁, we get

`[(1, 0.5),(0, 1)] A^-1 = [(0.5, 0),(-7, 2)]`

Applying R₁ → R₁ –`(1/2)` R₂, we get

`[(1, 0),(0, 1)] A^-1 = [(4, -1),(-7, 2)]`

∴ A^–1 = `[(4, -1),(-7, 2)]`