The value of `|[1,a,b+c],[1,b,c+a],[1,c,a+b]|` is

The value of Delta = |(1,a,b +c),(1,b,c +a),(1,c,a +b)| , is

Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|

If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|= (A) 1 (B) -1 (C) a+b+c (D) 0

If a b+b c+c a=0 , then what is the value of (1/(a^2-b c)+1/(b^2-c a)+1/(c^2-a b)) ? (a) 0 (b) 1 (c) 3 (d) a+b+c

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

Show without expanding that |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=|[1,b c, b+c],[1,c a, c+a],[1,a b, a+b]|

|[a, 1, b+c], [b, 1, c+a], [c, 1, a+b]|=?

Write the value of the determinant |a1b+c b1c+a c1a+b| .

If |a|=1,|b|=3 and |c|=5 , then the value of [a-b" "b-c" "c-a] is