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Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]]=(b-c)(c-a)(a-b) |
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Answer» SOLUTION :`[[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]]` `[[1,0,0],[b+c,a-b,b-c],[b^2+c^2,a^2-b^2,b^2-c^2]]` (REPLACING `C_2` and `C_3` by `C_3-C_1` and `C_3-C_2` RESPECTIVELY.) =`1XX[[a-b,b-c],[a^2-b^2,b^2-c^2]]` (a-b)(b-c)`[[1,1],[a+b,b+c]]` (a-b)(b-c)(b+c-a-b) (a-b)(b-c)(c-a)=R.H.S. |
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