freepeople性欧美熟妇, 色戒完整版无删减158分钟hd, 无码精品国产vα在线观看DVD, 丰满少妇伦精品无码专区在线观看,艾栗栗与纹身男宾馆3p50分钟,国产AV片在线观看,黑人与美女高潮,18岁女RAPPERDISSSUBS,国产手机在机看影片

正文內(nèi)容

第一章行列式-文庫吧資料

2025-07-28 09:41本頁面
  

【正文】 ?????????211121100??ininiiii AaAaAa ???? ?2211? ?ni ,2,1 ??例 1 3351110243152113???????D03550100131111115?????? ? 31 2 cc ??34 cc ?0551111115)1( 33?????? ?055026115???5526)1( 31????? ?5028???.40?12 rr ? 證 用數(shù)學(xué)歸納法 21211xxD ?? 12 xx ?? ,)(12 ? ??? ?? ji ji xx)式成立.時(shí)(當(dāng) 12?? n例 2 證明范德蒙德 (Vandermonde)行列式 ??????????1112112222121).(111jinjinnnnnnnxxxxxxxxxxxD???????)1(,階范德蒙德行列式成立)對(duì)于假設(shè)( 11 ?n)()()(0)()()(0011111213231222113312211312xxxxxxxxxxxxxxxxxxxxxxxxDnnnnnnnnn?????????????????????就有提出,因子列展開,并把每列的公按第 )(1 1xx i ?)()())((211312 jjin innxxxxxxxxD ?????? ?????).(1 jjin ixx ?? ????223223211312111)())((???????nnnnnnxxxxxxxxxxxx??????? n1階范德蒙德行列式 推論 行列式任一行(列)的元素與另一行(列)的對(duì)應(yīng)元素的代數(shù)余子式乘積之和等于零,即 .ji,AaAaAa jninjiji ????? 02211 ?,11111111nnnjnjininjnjnjjaaaaaaaaAaAa??????????? ???證 行展開,有按第把行列式 jaD ij )d e t (?,11111111nnniniininjninjiaaaaaaaaAaAa??????????? ???可得換成把 ),1( nkaa ikjk ??行第 j行第 i,時(shí)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) ????????? 。kpkp ab ? 當(dāng) 時(shí) , jik ,?, ipjpjpip abab ??例如 推論 如果行列式有兩行(列)完全相同,則此行列式為零 . 證明 互換相同的兩行,有 .0?? D,DD ??? ? ? ? ,11 1tt ????故 ? ? .111 11 DaaaaDnij npjpippt ????? ? ???證畢 ,571571??266853.825825??361567567361266853性質(zhì) 3 行列式的某一行(列)中所有的元素都乘以同一數(shù) ,等于用數(shù) 乘此行列式 . k knnnniniinaaakakakaaaa?????????????????212111211nnnniniinaaaaaaaaak?????????????????212111211?推論 行列式的某一行(列)中所有元素的公因子可以提到行列式符號(hào)的外面. 性質(zhì)4 行列式中如果有兩行(列)元素成比例,則此行列式為零. 證明 nnnniniiiniinaaakakakaaaaaaa?????????????????????????21212111211nnnniniiiniinaaaaaaaaaaaak?????????????????????????21212111211?.0?性質(zhì) 5 若行列式的某一列(行)的元素都是兩數(shù)之和 . nnnininnniiniiaaaaaaaaaaaaaaaD??????????)()()(2122222211111211???????則 D等于下列兩個(gè)行列式之和: nnninnininnninniniaaaaaaaaaaaaaaaaaaD?????????????????????????122211111122211111例如 性質(zhì)6 把行列式的某一列(行)的各元素乘以同一數(shù)然后加到另一列 (行 )對(duì)應(yīng)的元素上去,行列式不變. njnjninjjinjiaaaaaaaaaaaa?????????????12222111111njnjnjninjjjinjjijiaakaaaaakaaaaakaaakrr?????????????)()()(1222221111111?????k例如 例1 2101044614753124025973313211???????????D應(yīng)用舉例 計(jì)算行列式常用方法:利用運(yùn)算 把行列式化為上三角形行列式,從而算得行列式的值 . ji krr ?3? ?2101044614753124025973313211???????????D3? ?解 2101044614753124022022013211312?????????? rr2101044614753140202022013211?????????2101044614753124022022013211312?????????? rr? ?2???? ?3???13 2rr ?? ??? 4?42 rr ?2220020220140203512013211????????? 2220035120140202022013211?????????14 4rr ?13 3rr ?2220001000211003512013211????????34 rr ?2220020220211003512013211?????????23 rr ??? ?2???6000001000211003512013211????????? ?? ?? ?612 ?????45 4rr ? .12?6400001000211003512013211????????35 2rr ?4??例 2 計(jì)算 階行列式 nabbbbabbbbabbbbaD??????????解 ? ?? ?? ?? ? abbbnababbnabbabnabbbbna?????????1111?????????D將第 都加到第一列得 n,3,2 ?? ?abbbabbbabbbbna?????????1111)1( ???? ?babababbbbna????????1)1(00? ? .)()1( 1????
點(diǎn)擊復(fù)制文檔內(nèi)容
環(huán)評(píng)公示相關(guān)推薦
文庫吧 www.dybbs8.com
備案圖鄂ICP備17016276號(hào)-1