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The rank of the matrix [[-1,2,5],[2,-4,a...

The rank of the matrix `[[-1,2,5],[2,-4,a-4],[1,-2,a+1]]` is (where a = - 6)

A

`2, if a=-6`

B

`2, if a=1`

C

`1, if a=2`

D

`1, if a=-6`

Text Solution

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The correct Answer is:
B, D
Let `A= [[-1, 2, 5],[2, -4, a-4],[1, -2, a+1]]`
Applying `R_(2) rarr R_(2) 2 R_(1) and R_(3) rarr R_(3) + R_(1)`, then
`A = [[-1, 2, 5],[0,0,a+6],[0,0,a+6]]`
Applying `R_(3) rarr R_(3) - R_(2)`, then
`A = [[-1, 2, 5],[0,0,a+6],[0,0,0]]`
For `a = - 6 , p (A) = 1`
For `a = 1,2,p (A) = 2`
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