Question

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

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

Answer 1

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

∴ |A| = `|(2,1),(7,4)| = 8 - 7 = 1 ne 0`

∴ A^-1 exists.

Consider AA^-1 = I

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

By R₁ → R₁ - `1/7`R₂ we get,

`[(1,3/7),(7,4)] "A"^-1 = [(1,(-1)/7),(0,1)]`

By R₂ → R₂ - 7R₁ we get,

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

By R₁ → R₁ - `3/7`R₂ 

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

∴ `"A"^-1 = [(4,-1),(-7,2)]`