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V. Matricer – 4. Determinanter 420 • 3-matrix a11 a12 a13 a21 a22 a23 = a11 a31 a32 a33 a22 a23 − a12 a32 a33 a21 a23 + a13 a31 a33 a21 a22 a31 a32 4.3. Udregn determinanter ☞ [LA] 8 Determinanter Eksempler −1 2 3 4 = (−1) · 4 − 2 · 3 = −10 1 2 3 4 5 6 2 3 0 = 1 · 5 6 3 0 − 2 · 4 6 2 0 + 3 · 4 5 2 3 = (5 · 0 − 6 · 3) − 2(4 · 0 − 6 · 2) +3(4 · 3 − 5 · 2) = −18 + 24 + 6 = 12 4.4. Nem vej til areal ☞ [LA] 8 Determinanter Eksempel
V. Matricer – 4. Determinanter 421 Areal a1 b1 Areal = (a1 + b1)(a2 + b2) − a1a2 − b1b2 − 2a2b1 = a1b2 − a2b1 = a1 a2 b1 b2 4.5. Determinant ved rækkeudvikling ☞ [LA] 8 Determinanter Definition Lad Aij være den (m − 1) × (n − 1)-matrix, der fremkommer ved at slette i-te række og j-te søjle i en m × n-matrix A. Determinanten af en kvadratisk n × n-matrix A er givet ved rækkeudvikling efter i-te række n |A| = (−1) i+j aij|Aij| j=1 b2 a2
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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 - 1. Kontinuitet
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1. Grafiske/numeriske metoder IV Di
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1. Vektorer og matricer V Matricer
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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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etningsafledede, 89, 102 retningsfe
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