《線性代數(shù)》同濟大學版 課后習題答案詳解

1、1《線性代數(shù)》同濟大學版《線性代數(shù)》同濟大學版課后習題答案詳解課后習題答案詳解第一章第一章行列式行列式1?利用對角線法則計算下列三階行列式?(1)?381141102???解381141102????2?(?4)?3?0?(?1)?(?1)?1?1?8?0?1?3?2?(?1)?8?1?(?4)?(?1)??24?8?16?4??4?(2)?bacacbcba解bacacbcba?acb?bac?cba?bbb?aaa?ccc?3abc

2、?a3?b3?c3?(3)?222111cbacba解222111cbacba?bc2?ca2?ab2?ac2?ba2?cb2?(a?b)(b?c)(c?a)?(4)?yxyxxyxyyxyx???解yxyxxyxyyxyx????x(x?y)y?yx(x?y)?(x?y)yx?y3?(x?y)3?x3?3xy(x?y)?y3?3x2y?x3?y3?x3??2(x3?y3)?2?按自然數(shù)從小到大為標準次序?求下列各排列的逆序數(shù)?(1)1

3、234?解逆序數(shù)為0(2)4132?解逆序數(shù)為4?41?43?42?32?(3)3421?解逆序數(shù)為5?32?31?42?4121?(4)2413?解逆序數(shù)為3?21?41?43?(5)13???(2n?1)24???(2n)?解逆序數(shù)為?2)1(?nn3解efcfbfdecdbdaeacab???ecbecbecbadf?????abcdefadfbce4111111111?????(4)?dcba100110011001???解dc

4、ba100110011001???dcbaabarr10011001101021??????????dcaab101101)1)(1(12???????01011123??????????cdcadaabdcc?abcd?ab?cd?ad?1?cdadab???????111)1)(1(235?證明:(1)?(a?b)31112222bbaababa?證明1112222bbaababa?00122222221213ababaabaaba

5、cccc???????????abababaab22)1(22213???????21))((abaabab?????(a?b)3?(2)yxzxzyzyxbabzaybyaxbxazbyaxbxazbzaybxazbzaybyax)(33???????????證明bzaybyaxbxazbyaxbxazbzaybxazbzaybyax?????????bzaybyaxxbyaxbxazzbxazbzayybbzaybyaxzbyaxb