The valaues of x for which the given mat...

The valaues of x for which the given matrix `[(-x,x,2),(2,x,-x),(x,-2,-x)]` will be non-singular are

A

`-2 le x le -2`

B

for all x other than 2 and `-2`

C

`x gt2`

D

`x le -2`

Text Solution

Verified by Experts

The correct Answer is:

B

The given matrix will be non-singular, if
`rArr |(-x,x,2),(2,x,-x),(x,-2,-x)|!= 0`
`rArr -x (-x^(2) -2x) -x (-2x + x^(2)) + 2(-4 -x^(2)) != 0`
`rArr 2x^(2) - 8x != 0 rArr x != +- 2`

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