Question

Find the inverse of the following by Gauss-Jordan method:

`[(2, -1),(5, -2)]`

Answer 1

A = `[(2, -1),(5, -2)]`

[A|I₂] = `[(2, -1, |, 1, 0),(5, -2, |, 0, 1)]`

`{:("R"_1 -> ("R"_1)/2),(->):} [(1, (-1)/2, |, 1/2, 0), (5, -2, |, 0, 1)]`

`{:("R"_2 -> "R"_2 - 5"R"_1),(->):} [(1, (-1)/2, |, 1/2, 0),(0, 1/2, |, -5/2, 1)]`

`{:("R"_2 -> 2"R"_2),(->):} [(1, (-1)/2, |, 1/2, 0),(0, 1, |, -5, 2)]`

`{:("R"_1 -> "R"_1 + 1/2 "R"_2),(->):} [(1, 0, |, -2, 1),(0, 1, |, -5, 2)]`

∴ A^–1 = `[(-2, 1),(-5, 2)]`