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)]`