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Question
Find the rank of the following matrices by minor method:
`[(1, -2, 3),(2, 4, -6),(5, 1, -1)]`
Solution
A = `[(1, -2, 3),(2, 4, -6),(5, 1, -1)]`
A is matrix of order 3 × 3 and P(A) ≤ 3
Third order minor `|(1, -2, 3),(2, 4, -6),(5, 1, -1)|`
= 1(– 4 + 6) + 2(– 2 + 30) + 3(2 – 20)
= 2 + 56 – 54
= 4 ≠ 0
∴ P(A) = 3
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