1)证明:在n维线性空间F[x]n中,多项式-|||-(x)=(x-(a)_(1))... (x-(a)_(i-1))cdot (x-(a)_(i+1))... (x-(a)_(n))-|||-=1, 2,···,n-|||-是一组基,其中a1,a2,···,an是数域F中n个互不相同的-|||-数;-|||-2)在1)中,取a 1,a2,···,an为全体n次单位根,求由基-|||-1,x,···, ^n-1 到基f1,···f2,···,fn的过渡矩阵.