Question

Find the rank of the following matrices by row reduction method:

`[(3, -8, 5, 2),(2, -5, 1, 4),(-1, 2, 3, -2)]`

Answer 1

A = `[(3, -8, 5, 2),(2, -5, 1, 4),(-1, 2, 3, -2)]`

`{:("R"_2 ↔ "R"_3),(->):} [(-1, 2, 3, -2),(2, -5, 1, 4),(3, -8, 5, 2)]`

`{:("R"_1 -> (-)"R"_1),(->):} [(1, -2, -3, 2),(2, -5, 1, 4),(3, -8, 5, 2)]`

`{:("R"_2 -> "R"_2 - 2"R"_1),("R"_2 -> "R"_3 - 3"R"_1),(->):} [(1, -2, -3, 2),(0, -1, 7, 0),(0, -2, 14, -4)]`

`{:("R"_3 -> "R"_3 - 2"R"_2),(->):} [(1, -2, -3, 2),(0, -1, 7, 0),(0, 0, 0, -4)]`

The last equivalent matrix is in row echelon form.

It has three non-zero rows.

∴ P(A) = 3