Question

n阶行列式计算 求过程

1 0 0....0 a1 0 1 0....0 a2 0 0 1....0 a3 ..... ..... ..... 0 0 0....1 an b1 b2 b3.....bn c

Answer 1

这是n+1阶行列式哦。
设原式=┃An┃
沿第一列展开得
┃An┃=┃An-1┃+（-1）^(n+2)b1*(-1)^(n+1)a1┃E┃

=┃An-1┃-a1b1

=┃An-2┃-(-1)^(n+1)b2*(-1)^na2┃E┃-a1b1

=┃An-2┃-a2b2-a1b1

=....

=c-∑akbk(k=1,2,...,n)