1.

`Delta = |(a =x,b,c),(b,x +c,a),(c,a,x +b)|`. Which of the following is a factor for the above determinant ?A. `x -(a + b +c)`B. `x + (a +b +c)`C. `a + b + c`D. `-(a +b +c)`

Answer» Correct Answer - B
We have,
`Delta = |(a +x,b,c),(b,x +c,a),(c,a,x + b)|`
`rArr Delta = |(x + a + b + c,b,c),(x +a + b + c,x +c,a),(x + a + b + c,a,x +b)|` Applying `C_(1) rarr C_(1) + C_(2) + C_(3)`
`rArr Delta = (x +a +b +c) |(1,b,c),(1,x +c,a),(1,a,x +b)|`
`rArr (x +a +b +c)` is a factor of `Delta`


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