Question

Find the rank of the following matrices by minor method:

`[(1, -2, 3),(2, 4, -6),(5, 1, -1)]`

Answer 1

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