《線性代數(shù)》同濟(jì)大學(xué)版 課后習(xí)題答案詳解

1、1《線性代數(shù)》同濟(jì)大學(xué)版《線性代數(shù)》同濟(jì)大學(xué)版課后習(xí)題答案詳解課后習(xí)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(jì)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(biāo)準(zhǔn)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