" (iii) "(a-b)" is a factor of the following determinant "|[1,a,a^(2)],[b,b,b^(2)],[1,c,c^(2)]|

" 0.The value of the determinant "|[1,x,x^(2)],[1,b,b^(2)],[1,c,c^(2)]|" is: "

Show that a-b is a factor of |[1,a,a^(2)],[1,b,b^(2)],[1,c,c^(2)]|

The value of the determinant |{:(1,a, a^(2)-bc),(1, b, b^(2)-ca),(1, c, c^(2)-ab):}| is…..

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

Find the factor of determinant |(a, b+c, a^2), (b, c+a, b^2), (c, a+b, c^2)|.

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

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]|. 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

If a , b , c are unequal , what is the condition that value of the following determinant is zero ? Delta=|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|