Evaluate the following: ` |[1, a, b+c],[1, b, c+a],[1, c, a+b]| `

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

|[a, 1, b+c], [b, 1, c+a], [c, 1, a+b]|=?

Match the following. (A) 1-c, 2-b, 3-a (B) 1-b, 2-c, 3-a (C) 1-a, 2-b, 3-c (D) 1-a, 2-c, 3-b

Without expanding, prove that each of the following determinant vanishes : |(1,a,b+c),(1,b,c+a),(1,c,a+b)|

Prove the following : |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

Prove the following : |{:(bc,a,1),(ca,b,1),(ab,c,1):}|=(a-b)(b-c)(a-c)

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: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|

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