Question

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

`[(1, -1, 0),(1, 0, -1),(6, -2, -3)]`

Answer 1

A = `[(1, -1, 0),(1, 0, -1),(6, -2, -3)]`

[A|I₃] = `[(1, -1, 0, |, 1, 0, 0),(1, 0, -1, |, 0, 1, 0),(6, -2, -3, |, 0, 0, 1)]`

`{:("R"_2 -> "R"_2 - "R"1),("R"_3 -> "R"_3 - 6"R"_1),(->):} [(1, -1, 0, |, 1, 0, 0),(0, 1, -1, |, 0, 1, 0),(0, 4, -3, |, -6, 0, 1)]`

`{:("R"_3 -> "R"_3  -> 4"R"_2),(->):} [(1, -1, 0, |, 1, 0, 0),(0, 1, -1, |, -1, 1, 0),(0, 0, 1, |, -2, -4, 1)]`

`{:("R"_2 -> "R"_2 + "R"_3),(->):} [(1, -1, 0, |, 1, 0, 0),(0, 1, 0, |, -3, -3, 1),(0, 0, 1, |, -2, -4, 1)]`

`{:("R"_1 -> "R"_1 + "R"_2),(->):} [(1, 0, 0, |, -2, -3, 1),(0, 1, 0, |, -3, -3, 1),(0, 0, 1, |, -2, -4, 1)]`

A^–1 = `[(-2, -3, 1),(-3, -3, 1),(-2, -4, 1)]`