InterviewSolution
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InterviewSolution
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Show that :`|x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot` |
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Answer» `|(x,y,z),(x^2,y^2,z^2),(x^3 , y^3,z^3)|` `= xyz|(1,1,1),(x,y,z),(x^2,y^2,z^2)|` `c_2 -> c_2 - c_1` `c_3 -> c_3 - c_1` `=> |(1,0,0),(x, y-x, z-x),(x^2, y^2-x^2, z^2-x^2)|` `= 1((y-x)(z^2-x^2) - (z-x)(y^2 - x^2))` `= xyz(y-x)(z-x)(z+x-y-x)` `= xyz(y-x)(z-x)(z-y)`= RHS hence proved |
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