［急!］帮忙解答一道行列式求值的题!

题目

［急!］帮忙解答一道行列式求值的题!
N*N的行列式,对角线上全是a,上三角全是b,下三角全是-b.
a b b b--- b
-b a b b---b
-b -b a---- b
--- -- -- -- -b
-b -b -b ---- a

答案

按第1列分拆成2个行列式的和Dn = b b b ...b a-b b b ...b-b a b ...b 0 a b ...b-b -b a ...b + 0 -b a ...b............-b -b -b ...a 0 -b -b ...a第1个行列式:ri+r1,i=2,3,...,n所有行加第1行,变为上三角行列式...