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V. Matricer – 4. Determinanter 426 4.13. Test determinant nul Test ☞ [LA] 8 Determinanter Gælder der altid, at determinanten −1 3 0 x y z −1 3 = 0. 0 Løsning Første og tredje søjle er ens. Afkryds: ja nej 4.14. Udregn determinanter Eksempler “Reducer til øvre trekantsmatrix” ☞ [LA] 8 Determinanter 1) −1 3 2 4 = −1 0 2 10 = (−1) · 10 = −10 2) 1 4 2 2 5 3 3 6 0 = 1 0 0 2 −3 −1 3 −6 −6 = 1 0 0 2 −3 0 3 −6 −4 = 1 · (−3) · (−4) = 12
V. Matricer – 4. Determinanter 427 4.15. Determinant af matrixprodukt ☞ [LA] 8 Determinanter Sætning 11 (Produktreglen) For to kvadratiske n × n-matricer A,B gœlder |AB| = |A||B| Bevis ForBfast ogAen rækkeoperationsmatrix er produktreglen netop rækkeregnereglerne. Ved rækkereduktion kan A skrives som produkt af rækkeoperations-matricer samt enten identitetsmatricen eller en matrix med en 0-række nederst. Produktreglen følger heraf. 4.16. Brug produktreglen Eksempel ☞ [LA] 8 Determinanter 15 |AA| = 36 14 21 51 19 1 2 3 |A| = 4 5 6 = 12 2 3 0 15 42 = |AA| = |A| · |A| = 12 · 12 = 144 24
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 7. Lagrangemet
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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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