同济大学线性代数第六版答案(3)

(2n1)2(2n1)4(2n1)6

(2n1)(2n2) (n1个)

(6)1 3 (2n1) (2n) (2n2) 2

解逆序数为n(n1)

3 2(1个)

5 2 5 4 (2个)

(2n1)2(2n1)4(2n1)6

(2n1)(2n2) (n1个)

4 2(1个)

6 2 6 4(2个)

(2n)2 (2n)4 (2n)6 (2n)(2n2) (n1个)

3写出四阶行列式中含有因子a11a23的项

解含因子a11a23的项的一般形式为

(1)t a11a23a3r a4s

其中rs是2和4构成的排列这种排列共有两个即24和42

所以含因子a11a23的项分别是

(1)t a11a23a32a44(1)1a11a23a32a44a11a23a32a44

(1)t a11a23a34a42(1)2a11a23a34a42a11a23a34a42