1.3.2-利用行列性质降阶计算行列式

利用行列式性质降阶计算行列式例14计算dcdcdcbababaDn2aDn2解法一bd0dcdcba0ba0cdcdcbaba0d0dcdcba0baaDn20cdcdcbaba0bdcdcbabaaddcdcbababc22)(nDbcad422)(nDbcad21)(...Dbcadnnbcad)(dcdcdcbababaDn2解法二212121///000nnnnrcarrcarrcarabababbcdabcdabcda-+----=--ONNO()nadbc=-例15证明Vandermonde行列式1112112222121)(.....................1...11jinjinnnnnnnxxxxxxxxxxxD注：“∏”表示求积。1212212)(11jijixxxxxxD证用数学归纳法，n=2时，Vandermonde行列式结果成立,现假设对n-1阶Vandermonde行列式结果成立,证明对n阶Vandermonde行列式结果也成立。为此，设法把Dn降阶：0...)()(............0...)()(0...1...11222211221121......21112nnnnnnnnrxrrxrrxrnxxxxxxxxxxxxxxxxDnnnnnnn2112222111122111211)(...)()(............)(...)()(...)1(nnnnnnnnnnnnnnnnnnxxxxxxxxxxxxxxxxxxxxxxxx212221121121..................1...11))...()((nnnnnnnnnxxxxxxxxxxxx11121)())...()((jinjinnnnxxxxxxxx1)(jinjixx