[" (i) "(a+b+c)" is a factor of the following determinant ":|[a,b,c],[b,c,a],[c,a,b]|]

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

Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]

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

Factorize the following: |[x+a,b,c], [b,x+c,a] , [c,a,x+b]|

Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

A factor of the determinant |(x+a,b,c),(a,x+b,c),(a,b,x+c)| is

Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

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