Question

Find the inverse of the following matrix (if they exist):

`((1,3),(2,7))`

Answer 1

Let A = `[(1,3),(2,7)]`

∴ |A| = `|(1,3),(2,7)|`

= 7 − 6 

= 1 ≠ 0

∴ A⁻¹ exists.

Consider AA⁻¹ = I

∴ `[(1,3),(2,7)] A^-1 = [(1,0),(0,1)]`

By R₂ − 2R₁, we get,

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

By R₁ - 3R₂ we get,

`[(1,0),(0,1)] A^-1 = [(7,-3),(-2,1)]`

A⁻¹ = `[(7,-3),(-2,1)]`