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Question
Find the rank of the following matrices
`((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
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Solution
Let A = `((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
Let us transform the matrix A to an echelon form by using elementary transformations.
A = `((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
`∼ ((1, 2, -1, 3),(0, 0, 3, -8),(0, 0, 6, -16)) {:("R"_2 -> "R"_2 - 2"R"_1),("R"_3 -> "R"_3 - 3"R"_1):}`
`∼ ((1, 2, -1, 3),(0, 0, 3, -8),(0, 0, 0, 0)) {:"R"_3 -> "R"_3 - 3"R"_1:}`
The above matrix is in echelon form.
The number of non zero rows is 2
⇒ p(A) = 2
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