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Question
Find the rank of the following matrices
`((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Solution
Let A = `((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Order of A is 3 × 3
∴ p(A) ≤ 3
Consider the third order minor = `|(-1, 2, -2),(4, -3, 4),(-2, 4, -4)|`
= – 1(12 – 16) – 2(– 16 + 8) – 2(16 – 6)
= – 1(– 4) – 2(– 8) – 2(10)
= 4 + 16 – 20
= 0
Since the third order minor vanishes, therefore
∴ p(A) ≠ 3
Consider a second order minor = `|(-1, 2),(4, -3)|`
= 3 – 8
= – 5 ≠ 0
There is a minor of order 2, which is not zero.
∴ p(A) = 2
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