[" [Hint : "1250" - "],[[" (ix) "|[1,a,b+c],[1,b,c+a],[1,c,a+b]]]

Evaluate [[1,a,b+c],[1,b,c+a],[1,c,a+b]]

The value of |[[1,a,b+c],[1,b,c+a],[1,c,a+b]]| is

|(1,a,b+c),(1,b,c+a),(1,c,a+b)| =

|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

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

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]|

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

|(1+a,b,c),(a,1+b,c),(a,b,1+c)|=