Find the rank of `[[1,1,1],[a,b,c],[a^2,b^2,c^2]]`

find the rank of [[1,1,1],[a,b,c],[a^3,b^3,c^3]]

(b) Find the rank of the matrix [[1,-1,2,-1],[4,2,-1,2],[3,2,-2,0]]

Find the value of det[[1,a,a^(2)-bc1,b,b^(2)-ac1,c,c^(2)-ab]]

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)| .

Find the value of: |[1 a^2 a^3],[1 b^2 b^3],[1 c^2 c^3]|

If the rank of the matrix [[-1,2,5],[2,-4,a-4],[1,-2,a+1]] is 1 then the value of a is (A) -1 (B) 2 (C) -6 (D) 4

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]|

Prove that |[1,a,bc] , [1,b,ca], [1,c,ab]|=|[1,a,a^2] , [1,b,b^2] , [1,c,c^2]|

Evaluate: :det[[1,a,a^(2)1,b,b^(2)1,c,c^(2)]]