《線性代數(shù)》郝志峰習題詳解

1、習題一習題一1、（1）.????????110202112501220322211350021235??????????????????????????D（2）.33323???????????????????????abcDbcaabcbaccbacccaaabbbabcabccab2、（1）排列的逆序數(shù)為.00235????（2）排列的逆序數(shù)為.??????1012212??????????nnnn3、含有因子的項（縱標為1324，

2、逆序數(shù)為），1123aa11233244?aaaa00101????11233442aaaa（縱標為1342，逆序數(shù)為）.00022????4、經(jīng)第一行與第四行交換行列式為負號，經(jīng)轉(zhuǎn)置行列式不變，經(jīng)用2乘所有元素為，52經(jīng)用乘第2列加到第5列為行列式不變，經(jīng)這些處置后行列式為.??1?32?D5、的代數(shù)余子式為0，的代數(shù)余子式為.31a11a????11103326??????????6、????????????????31323334

3、125113107114103043???????????????????????????D.7、（1）.??????4321111248??????????D（2）121223443000001111110000001111011????????xxxrrccxxxDrrccyyyyy.????21222100100101按第一行展開按第一列展開??????xyxyxxyyy8、（1）.????????11111100020n11!0

4、01按第行展開????????????????nnnnDnnn??????????00123012120121112012111121201210121100010001000100010100111.按展開??????????????????????????????????????????????????????????????????:??????nnnnnnnnnnnnnnnnnnnnnnnnaaxaDaxaxaaxaxaxara

5、xaxaxaaxaxaxaaxaxaxa10、（1）用數(shù)學歸納法去證.當時，，2?n??3322221????????????abababDababaabbabab當時，1??nk111200010001000001????????????????????????kkkkkkababababababDDabababab當時，，?nk????111112???????????????????kkkkkkkkkabababDabDabDab