線性代數(shù)課件ch2-2華東理工大學(xué)-閱讀頁
2024-08-20 15:59本頁面
【正文】 152113???????D3351110243152113???????D03550100131111115?????對解于是工作量相對較小化為零的，所以將該行其它元素行有考慮到第,03? ?231 ?c)1(34cD0551111115)1( 33?????? ?055026115???5526)1( 31????? ?5028???.40?)1(12r.解畢性質(zhì) 5 行列式任一行（列）的元素與另一行（列）的對應(yīng)元素的代數(shù)余子式乘積之和等于零，即 ).(,02211 jiAaAaAa jninjiji ????? ?,11111111nnnjnjininjnjnjjaaaaaaaaAaAa??????????? ???證 行展開，有按第把行列式 jA,11111111nnniniininjninjiaaaaaaaaAaAa??????????? ???可得換成把 ),1( nkaa ikjk ??行第 j行第 i,時所以當(dāng) ji ?).(,02211 jiAaAaAa jninjiji ????? ?同理 ).(,02211 jiAaAaAa njnijiji ????? ?相同 關(guān)于代數(shù)余子式的重要性質(zhì) ???????? 。nij ikiA j kaAjk?? ?? ????當(dāng)當(dāng)階行列式已知例 52mB ?????5701033555680122244412111.4544 AA ?試求代數(shù)余子式之和行展開，得按行列式的第解 4)1(33555 4544434241 mAAAAA ?????，即得式作乘積之和，由性質(zhì)行對應(yīng)元素的代數(shù)余子行與第再用行列式的第542)2(022444 4544434241 ????? AAAAA兩式，、聯(lián)立 )2()1()1(33555 4544434241 mAAAAA ?????)2(022444 4544434241 ????? AAAAA?????? ??x4?????y2???????02435yxmyx即解得.1124544 myAA ????例 3 nnnnnknkkkkkbbbbccccaaaaD????????????1111111111110?設(shè),11111kkkkaaaaD????? ,11112nnnnbbbbD?????.21 DDD ?證明 證明
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