If `A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]|` , `B=|[1,bc, a],[1,ca, b],[1,ab, c]|` , then

Options

A. `Delta_(1) + Delta_(2) =0`
B. `Delta_(1) + 2Delta_(2) = 0`
C. `Delta_(1) = Delta_(2)`
D. none of these

Answer

A

Explanation

We have,
`Delta_(2) = |(1,bc,a),(1,ca,b),(1,ab,c)|` ltrbgt `rArr Delta_(2) = (1)/(abc)|(a,abc,a^(2)),(b,abc,b^(2)),(c,abc,c^(2))| "Applying " R_(1) rarr R_(1) (a) " " R_(2) rarr R_(2) (b) " " R_(3) rarr R_(3) (c)`
`rArr Delta_(2) = |(a,1,a^(2)),(b,1,b^(2)),(c,1,c^(2))|` [Taking abc common from `C_(2)`]
`rArr Delta_(2) = -|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|` [Interchanging `C_(1) and C_(2)`]
`rArr Delta_(2) = - |(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))| = - Delta_(1) rArr Delta_(1) + Delta_(2) = 0`