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Question
Find the rank of the following matrices
`((2, -1, 1),(3, 1, -5),(1, 1, 1))`
Solution
Let A = `((2, -1, 1),(3, 1, -5),(1, 1, 1))`
Order of A is 3 × 3
∴ p(A) ≤ 2
Consider the third order minor = `|(2, -1, 1),(3, 1, -5),(1, 1, 1)|`
= 2(1 + 5) – (– 1) (3 + 5) + 1 (3 – 1)
= 2 (6) + 1(8) + 1(2)
= 12 + 8 + 2
= 22 ≠ 0
There is a minor of order 3, which is not zero
∴ p(A) = 3
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