Find the value of the determinant.
`[[-a,a,a],[b,-b,b],[c,c,-c]]`

Find the values of A,B and C

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

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

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

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.

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]| . The other factor in the value of the determinant is

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a, a+b ,a+c],[ b+a,-2b,b+c],[c+a, c+b, -2c]|dot The other factor in the value of the determinant is (a) 4 (b) 2 (c) a+b+c (d) none of these

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

Without expanding at any stage, find the value of the determinant : Delta=|(20,a,b+c),(20,b,a+c),(20,c,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