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]| .

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

If a, b, c are positive and unequal, show that value of the determinant Delta=|a b c b c a c a b| is negative.

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

What is the value of the following determinant? Delta=|[4,a, b+c],[4,b, c+a],[4,c, 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):}|

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

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

If a ,b ,c are sides of a scalene triangle, then value of |[a, b, c] ,[b, c, a] ,[c, a, b]| is positive (b) negative non-positive (d) non-negative

|{:(a,b,c),(b,c,a),(c,a,b):}| is equal to