Question

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

`[(1, 1, 1, 3),(2, -1, 3, 4),(5, -1, 7, 11)]`

Answer 1

A = `[(1, 1, 1, 3),(2, -1, 3, 4),(5, -1, 7, 11)]`

`{:("R"_2 -> "R"_2 - 2"R"_1),("R"_3 -> "R"_3 - 5"R"_1),(->):}  [(1, 1, 1, 3),(0, -3, 1, -2),(0, -6, 2, -4)]`

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

The last equivalent matrix is in row echelon form.

It has two non-zero rows.

∴ P(A) = 2