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Article #71Re: Determinanten
From: Markus Hagen
Date: Tue, 13 May 2003 17:53
Date: Tue, 13 May 2003 17:53
36 lines
2102 bytes
2102 bytes
Markus Hagen wrote:
> n
> A = (a_ij) => det A = SUM (-1)^(1+j) * a_1j * det A_1j.
> j=1
Ich verga� zu erw�hnen, da� die Matrix A_1j aus der Matrix A durch
Streichen der 1-ten Zeile und j-ten Spalte entsteht.
ein kleines Beispiel:
/ 1 1 -1 \ (entwickeln von A nach der 3-ten Zeile)
A = | 2 -2 2 |
\ 3 0 -1 /
A_3j entsteht aus A durch streichen der 3-ten Zeile und j-ten Spalte:
A_31 = / 1 -1 \ => det A_31 = 2-2 = 0
\ -2 2 /
A_32 = / 1 -1 \ => det A_31 = 2-(-2) = 4
\ 2 2 /
A_33 = / 1 1 \ => det A_31 = -2-2 = -4
\ 2 -2 /
3
det A = SUM (-1)^3+j * a_3j * det A_3j
j=1
det A = (+1)*3*0 + (-1)*0*4 + (+1)*(-1)*(-4) = 4
Gru�
Markus (hoffe da hat sich kein Fehler eingeschlichen)
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X-Google-Language: GERMAN,ASCII X-Google-Thread: f6df2,f02e2166efef6d8e X-Google-Attributes: gidf6df2,public X-Google-ArrivalTime: 2003-05-13 10:55:14 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!sn-xit-02!sn-xit-06!sn-xit-09!supernews.com!news.maxwell.syr.edu!newsfeed.icl.net!newsfeed.fjserv.net!colt.net!peernews3.colt.net!news0.de.colt.net!news-fra1.dfn.de!fu-berlin.de!newsfeed01.sul.t-online.de!newsmm00.sul.t-online.com!t-online.de!news.t-online.com!not-for-mail From: "Markus Hagen" <Pi_is_3.1415926535897932385@t-online.de> Newsgroups: bln.sci.mathematik Subject: Re: Determinanten Date: Tue, 13 May 2003 19:53:52 +0200 Organization: T-Online Lines: 37 Message-ID: <b9rbfh$l0k$01$1@news.t-online.com> References: <b9r6t9$m6qcb$1@ID-118975.news.dfncis.de> <b9r9ii$hh8$05$1@news.t-online.com> Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Trace: news.t-online.com 1052848434 01 21524 PY+9EUQVS7YPp8 030513 17:53:54 X-Complaints-To: abuse@t-online.com X-ID: GhpLEcZGweNzytm20G4vxWZR6uvsseDLtN1A+9mIT0lHQ0JCa22xE7 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106