the value of the determinant
`|{:((a_(1)-b_(1))^(2),,(a_(1)-b_(2))^(2),,(a_(1)-b_(3))^(2),,(a_(1)-b_(4))^(2)),((a_(2)-b_(1))^(2),,(a_(2)-b_(2))^(2) ,,(a_(2)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(3)-b_(1))^(2),,(a_(3)-b_(2))^(2),,(a_(3)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(4)-b_(1))^(2),,(a_(4)-b_(2))^(2),,(a_(4)-b_(3))^(2),,(a_(4)-b_(4))^(2)):}|` is

Options

A. dependant on `a_(i),i=1,2,3,4`
B. dependant on `b_(i),i=1,2,3,4`
C. dependant on `a_(ij), b_(i) i= 1,2,3,4`
D. 0

Answer

D

Explanation

the given determinant on simplification gives
`Delta_(1) = |{:(a_(1)^(2),,-2a_(1),,1,,0),(a_(2)^(2),,-2a_(2),,1,,0),(a_(3)^(2),,-2a_(3),1,,0,),(a_(4)^(2),,-2a_(4),,1,,0):}|xx |{:(1,,b_(1),,b_(1)^(2),,0),(1,,b_(2),,b_(2)^(2),,0),(1,,b_(3),,b_(3)^(2),,0),(1,,b_(4),,b_(4)^(2),,0):}|`
`=0xx0 =0`