Question

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

`[(3,-10),(2,-7)]`

Answer 1

Let A = `[(3,-10),(2,-7)]`

∴ |A| = `|(3,-10),(2,-7)| = - 21 + 20 = - 1 ne 0`

∴ A^-1 exists.

Consider AA^-1 = I

∴ `[(3,-10),(2,-7)] "A"^-1 = [(1,0),(0,1)]`

By R₁ - R₂, we get,

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

By R₂ - 2R₁, we get,

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

By (- 1)R₂, we get,

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

By R₁ + 3R₂, we get,

`[(1,0),(0,1)] "A"^-1 = [(7,-10),(2,-3)]`

∴ `"A"^-1 = [(7,-10),(2,-3)]`