The value of the determinant `|[a-b,b+c,a],[b-c,c+a,b],[c-a,a+b,c]|` is

The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b, c]| is (a) a^3+b^3+c^3 (b) 3\ b c (c) a^3+b^3+c^3-3a b c (d) none

Let a ,b ,c be positive and not all equal. Show that the value of the determinant |[a, b, c],[b, c, a],[ c, a ,b]| is negative.

Write the value of the determinant |[a,1,b+c], [b,1,c+a] ,[c,1,a+b]| .

If a ne b ne c are all positive, then the value of the determinant |{:(a,b,c),(b,c,a),(c,a,b):}| is

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |[a, b, c], [b, c, a], [c, a, b]|

Write the value of the following determinant |(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|

The value of the determinant |(b +c,a -b,a),(c +a,b -c,b),(a +b,c -a,c)| , is

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

The vlaue of the determinant |(b+c, a, a),(b, c+a, b),(c,c,a+b)| (A) depends on a (B) depends on b (C) depends on c (D) dependent of a,b,c

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|