InterviewSolution
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InterviewSolution
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Prove that `Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}|` `= 2(a-b)(b-c)(c-1)` |
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Answer» `Delta = |{:(1,,1,,1),(a,,b,,c),(bc+a^(2),,ac+b^(2),,ab+c^(2)):}|` ` |{:(1,,1,,1),(a,,b,,c),(bc,,ac,,ab):}|+|{:(1,,1,,1),(a,,b,,c),(a^(2),,b^(2),,b^(2)):}|` `" Now " |{:(1,,1,,1),(a,,b,,c),(bc,,ac,,ab):}|` `=(1)/(abc) |{:(a,,b,,c),(a^(2),,b^(2),,c^(2)),(abc,,abc,,abc):}|" "underset("a,b,c respectively]")("[Multiplying "C_(1),C_(2),C_(3)" by")` `=|{:(a,,b,,c),(a^(2),,b^(2),,c^(2)),(1,,1,,1):}|` `=|{:(1,,1,,1),(a,,b,,c),(a^(2),,b^(2),,c^(2)):}|` `rArr Delta =2 |{:(1,,1,,1),(a,,b,,c),(a^(2),,b^(2),,c^(2)):}| = 2(a-b)(b-c)(c-a)` |
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