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If the inverse of the matriix [(alpha,14...

If the inverse of the matriix `[(alpha,14,-1),(2,3,1),(6,2,3)]` does not exist, then the vlaue of `alpha` is

A

1

B

`-1`

C

`0`

D

`-2`

Text Solution

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The correct Answer is:
D
Let `A=[{:(alpha,14,-1),(2,3,1),(6,2,3):}]`
`rArr |A| = [{:(alpha,14,-1),(2,3,1),(6,2,3):}]=alpha(9-2)-14(6-6)-1(4-18)`
`=7alpha - 0 + 1 xx14`
`|A| = 7alpha + 14`
It is given that inverse of A does not exists.
`:. |A| = 0`
`rArr 7 alpha + 14 = 0`
`rArr alpha = - 2`
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