计算N阶行列式的值.a23Ln1a+13Ln12a+2LnLLL123La+n-1

Question

计算N阶行列式的值. a 2 3 L n 1 a+1 3 L n 1 2 a+2 L n L L L 1 2 3 L a+n-1

Answer 1

若a=1,行列式1,2行相等,行列式=0若a≠1ri-r1,i=2,3,...,n (所有行减第1行)a 2 3 ...n -a a-1 0 ...0 -a 0 a-1 ...0 ......-a 0 0 ...a-1 c1 - [a/(a-1)]ci,i=2,3,...,nx 2 3 ...n 0 a-1 0 ...0 0 0 a-1 ...0 ......0...