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[a,b+c,a^(2)],[b,c+a,b^(2)],[c,a+b,c^(2)...

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

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det[[a,b+c,a^(2)b,c+a,b^(2)c,a+b,c^(2)]]

Prove that det[[a,b+c,a^(2)b,c+a,b^(2)c,a+b,c^(2)]]=-(a+b+c)xx(a-b)(b-c)(c-a)

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

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

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

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b c-a^2],[a b-c^2,b c-a^2,a c-b^2]| is a. always positive b. always negative c. always zero d. cannot say anything

The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b c-a^2],[a b-c^2,b c-a^2,a c-b^2]| is a. always positive b. always negative c. always zero d. cannot say anything