The value of the determinant `|{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x^(2)),(z^(2),1,x^(2)+y^(2)):}|` is :

Options

A. 0
B. `x^(2)+y^(2)+z^(2)`
C. `x^(2)+y^(2)+z^(2)+1`
D. None of the above

Answer

A

Explanation

Let `Delta=|(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x^(2)),(z^(2),1,x^(2)+y^(2))|`
Applying `C_(1)rarrC_(1)+C_(3)`.
`Delta|(x^(2)+y^(2)+z^(2),1,y^(2)+z^(2)),(x^(2)+y^(2)+z^(2),1,z^(2)+x^(2)),(x^(2)+y^(2)+z^(2),1,x^(2)+y^(2))|`
`Delta=(x^(2)+y^(2)+z^(2))|(1,1,y^(2)+z^(2)),(1,1,z^(2)+x^(2)),(1,1,x^(2)+y^(2))|`
`Delta=0[because C_(1) & C_(2)" are identical"]`