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Question
Find the rank of the following matrices by row reduction method:
`[(1, 1, 1, 3),(2, -1, 3, 4),(5, -1, 7, 11)]`
Solution
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
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