Fi(X)是一个不超过n-2次的多项式(i=1,2...N)求证对于任意n个数a1,a2.an有行列式F1(a1) F1(a2) F1(a3) … F1(an) ||F2(a1) F2(a2) F2(a3) … F2(an) ||F3(a1) F3(a2) F3(a3) … F3(an) ||… … … … … ||Fn(
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![Fi(X)是一个不超过n-2次的多项式(i=1,2...N)求证对于任意n个数a1,a2.an有行列式F1(a1) F1(a2) F1(a3) … F1(an) ||F2(a1) F2(a2) F2(a3) … F2(an) ||F3(a1) F3(a2) F3(a3) … F3(an) ||… … … … … ||Fn(](/uploads/image/z/3149059-67-9.jpg?t=Fi%28X%29%E6%98%AF%E4%B8%80%E4%B8%AA%E4%B8%8D%E8%B6%85%E8%BF%87n-2%E6%AC%A1%E7%9A%84%E5%A4%9A%E9%A1%B9%E5%BC%8F%EF%BC%88i%3D1%2C2...N%29%E6%B1%82%E8%AF%81%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8Fn%E4%B8%AA%E6%95%B0a1%2Ca2.an%E6%9C%89%E8%A1%8C%E5%88%97%E5%BC%8FF1%28a1%EF%BC%89+F1%28a2%EF%BC%89+F1%28a3%EF%BC%89+%E2%80%A6+F1%28an%EF%BC%89+%7C%7CF2%28a1%EF%BC%89+F2%28a2%EF%BC%89+F2%28a3%EF%BC%89+%E2%80%A6+F2%28an%EF%BC%89+%7C%7CF3%28a1%EF%BC%89+F3%28a2%EF%BC%89+F3%28a3%EF%BC%89+%E2%80%A6+F3%28an%EF%BC%89+%7C%7C%E2%80%A6+%E2%80%A6+%E2%80%A6+%E2%80%A6+%E2%80%A6+%7C%7CFn%28)
Fi(X)是一个不超过n-2次的多项式(i=1,2...N)求证对于任意n个数a1,a2.an有行列式F1(a1) F1(a2) F1(a3) … F1(an) ||F2(a1) F2(a2) F2(a3) … F2(an) ||F3(a1) F3(a2) F3(a3) … F3(an) ||… … … … … ||Fn(
Fi(X)是一个不超过n-2次的多项式(i=1,2...N)求证对于任意n个数a1,a2.an有行列式
F1(a1) F1(a2) F1(a3) … F1(an) |
|F2(a1) F2(a2) F2(a3) … F2(an) |
|F3(a1) F3(a2) F3(a3) … F3(an) |
|… … … … … |
|Fn(a1) Fn(a2) Fn(a3) … Fn(an) | 为零
Fi(X)是一个不超过n-2次的多项式(i=1,2...N)求证对于任意n个数a1,a2.an有行列式F1(a1) F1(a2) F1(a3) … F1(an) ||F2(a1) F2(a2) F2(a3) … F2(an) ||F3(a1) F3(a2) F3(a3) … F3(an) ||… … … … … ||Fn(
设 Fi(x)=bi0 + bi1x + bi2x^2 + ...+ bi,n-2 x^(n-2),i=1,2,...,n
令n阶矩阵 B=
b10 b11 ...b1,n-2 0
b20 b21 ...b2,n-2 0
......
bn0 bn1 ...bn,n-2 0
A =
1 1 ...1
a1 a2 ...an
a1^2 a2^2 ...an^2
......
a1^n-1 a2^n-1 ...an^n-1
则原行列式的矩阵 = BA等式两边取行列式,原行列式 = |B||A| = 0.
不知道