行列式 x -1 0.0 0 0 x -1.0 0 .0 0 0.x -1 a0 a1 a2..an-1 an
问题描述：
行列式 x -1 0.0 0 0 x -1.0 0 .0 0 0.x -1 a0 a1 a2..an-1 an
[x -1 0.....0 0][ 0 x -1.....0 0]...................[0 0 0....x -1] [a0 a1 a2..an-1 an]这是n+1阶行列式
答
c1+xc2+x^2c3+...+x^ncn+1行列式等于 0 -1 0 ...0 0 0 x -1 ...0 0...0 0 0 ...x -1a0+a1x+a2x^2+...+anx^n a1 a2 ..an-1 an按第1列展开,行列式 = (a0+a1x+a2x^2+...+anx^n)*(-1)^(n+1+1)*-1 0 ...0 0 x -1 ...0 0 ....