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Question
Find the rank of the following matrices by minor method:
`[(0, 1 ,2, 1),(0, 2, 4, 3),(8, 1, 0, 2)]`
Solution
A = `[(0, 1 ,2, 1),(0, 2, 4, 3),(8, 1, 0, 2)]`
A is matrix of order 3 × 4 and P(A) ≤ 3
Third order minor
`|(0, 1, 2),(0, 2, 4),(8, 1, 0)| = 0 - 1(0 - 32) + 2(0 - 16)`
= 32 – 32
= 0
`|(1, 2, 1),(2, 4, 3),(1, 0, 2)| = 1(8 - 0) - 2(4 - 3) + 1(0 - 4)`
= 8 – 2 – 4
= 2 ≠ 0
∴ P(A) = 3
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