[" Find the value of the following determinan "],[11quad aquad a^(2)-bc],[1quad bquad b^(2)-ca],[1quad cquad c^(2)=ab]|

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

|[(1)/(a),a^(2),bc],[(1)/(b),b^(2),ca],[(1)/(c),c^(2),ab]|=0

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

Find the values of each of the following expressions for a=1,b=2 and c=-1a^(3)+b^(3)+c^(3)-3abca^(2)+b^(2)+c^(2)-ab-bc-ca

Prove that |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)|= 0 .

Find the product of the following. (a^2+b^2+c^2-ab+bc+ca) (a+b-c)

Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

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

Without expanding determinant at any stage evaluate |(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|