InterviewSolution
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InterviewSolution
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Show that: `|a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot` |
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Answer» `= |(a,b-c,c+b),(a+c, b, c-a),(a-b,b+a, c)|` `c_1-> ac_1` `= 1/a |(a^2, b-c,c+b),(a^2+ac, b,c-a),(a^2 - ab, b+a, c)|` `c_1-> c_1 + bc_2 + c c_3` `=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)|` `r_2-> r_2- r_1 & r_3-> r_3- r_1` `= (a^2+b^2+c^2)/a |(1,b-c, c+b),(0,c,-(a+b)),(0,a+c,-b)|` `= (a^2 + b^2+c^2)/a [ (a+b)(a+c)- bc]` `= (a^2 + b^2 +c^2)/a [a^2 + ab+ac+bc-bc]` `= (a^2+b^2+c^2)(a+b+c)` hence proved |
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