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|[1/c,1/c,-(a+b)/c^2],[-(b+c)/c^2,1/a,1/...

`|[1/c,1/c,-(a+b)/c^2],[-(b+c)/c^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/(ac),(-b(a+b))/(ac^2)]|` is

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|[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/(ac),(-b(a+b))/(ac^2)]| is

|[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/(ac),(-b(a+b))/(ac^2)]| is (a) dependent on a,b,c (b) dependent on a (c) dependent on b (d) independent on a,b and c

((1)/(a)-(1)/(b+c))/((1)/(a)+(1)/(b+c))(1+(b^(2)+c^(2)-a^(2))/(2bc)):(a-b-c)/(abc)

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

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

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

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

a^(2)-b^(2)+c^(2)-1+2b-2ac

Prove: |[1,a^2+bc, a^3],[ 1,b^2+c a, b^3],[ 1,c^2+a b, c^3]|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

|{:(1,b+c,b^2+c^2),(1,c+a,c^2+a^2),(1,a+b,a^2+b^2):}|=(b-c)(c-a)(a-b)

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