InterviewSolution
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InterviewSolution
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Show that `|[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|=abc(a-b)(b-c)(c-a)` |
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Answer» `L.H.S. = |[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|` `= (abc)|[1,1,1],[a,b,c],[a^2,b^2,c^2]|` Applying `C_1->C_1-C_3 and C_2->C_2-C_3` `= (abc)|[0,0,1],[a-b,b-c,c],[a^2-b^2,b^2-c^2,c^2]|` `= (abc)(a-b)(b-c)|[0,0,1],[1,1,c],[a+b,b+c,c^2]|` `= (abc)(a-b)(b-c)[b+c-a-b]` `= (abc)(a-b)(b-c)(c-a) = R.H.S.` |
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