InterviewSolution
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InterviewSolution
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Prove that ` |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=(a+b+c)(a^2+b^2+c^2) ` |
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Answer» Apply `C_(1) to aC_(1) "and divide"Delta "by a` `therefore Delta = (1)/(a) * |[a^(2), b-c, c+b], [a^(2)+ac, b, c-a], [a^(2)-ab, b+a, c]|` ` = (1)/(a) |[a^(2)+b^(2)+c^(2), b-c, c+b], [a^(2) +b^(2)+c^(2), b, c-a], [a^(2) +b^(2)+c^(2), b+a, c]| ["applying "C_(1) to C_(1) + bC_(2) +cC_(3)]` |
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