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V. Matricer – 4. Determinanter 428 4.17. Determinant af potens ☞ [LA] 8 Determinanter Eksempel Potensers determinant −1 2 3 4 = (−1) · 4 − 2 · 3 = −10 k −1 2 = −1 2 3 4 3 4 k = (−10) k 4.18. Determinant af invers matrix ☞ [LA] 8 Determinanter Sætning 12 (Inversreglen) En kvadratisk matrix A er invertibel, hvis og kun hvis |A| = 0. Der gœlder hvis |A| = 0. |A −1 | = 1 |A| Bevis Hvis A er invertibel så giver produktreglen formlen. Hvis |A| = 0 så kan A skrives som produkt af rækkeoperations- matricer, som hver er invertible. A er da invertibel.
V. Matricer – 4. Determinanter 429 4.19. Brug inversreglen Eksempel ☞ [LA] 8 Determinanter Matricen ⎛ 1 2 ⎞ 3 A = ⎝4 5 6⎠ har determinant 2 3 0 |A| = 12 A er invertibel og den inverse har determinant |A −1 | = |A| −1 = 1 12 4.20. Test inversregel ☞ [LA] 8 Determinanter Test Determinanten af en invertibel matrix er altid = 0. Løsning Sætning 12 giver svaret direkte. Afkryds: ja nej 4.21. Test produktreglen ☞ [LA] 8 Determinanter
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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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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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