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Determine the values of x for which the ...

Determine the values of `x` for which the matrix `A=[x+1-3 4-5x+2 2 4 1x-6]` is singular.

A

`0,(3+-sqrt(205))/2`

B

`0,3/2`

C

`0,+-(sqrt(205))/2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Matrix `A=[(x+1,-3,4),(-5,x+2,2),(4,1,x-6)]` will be singular if
`|A|=|(x+1,-3,4),(-5,x+2,2),(4,1,x-6)|=0`
`implies(x+1)(x^(2)-4x-12-2)+3(-5x+30-8)`
`+4(-5-4x-8)=0`
`implies(x+1)(x^(2)-4x-14)+3(-5x+22)+4(-4x-13)=0`
`impliesx^(3)-4x-14x+x^(2)-4x-15x+66-16x-52=0`
`implies x(x^(2)-3x-48)=0`
`impliesx=0, x=(3+-sqrt(9+196))/(2xx1)`
`:.x=0, (3+-sqrt(205))/2`
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