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V. Matricer – 4. Determinanter 422 Kan skrives |A| = (−1) i+1 ai1|Ai1| + (−1) i+2 ai2|Ai2| + · · · 4.6. Determinant mange veje ☞ [LA] 8 Determinanter • Determinanten kan beregnes ved søjleudvikling n |A| = i=1 (−1) i+j aij|Aij| • Determinanten er uafhængig af valgt række/søjle. • Eksempel ⎛ 1 2 ⎞ 3 ⎝4 5 6⎠ 7 8 9 12 ⎛ − ∗ ⎞ − = ⎝4 | 6⎠ = 7 | 9 4 6 7 9 4.7. Udregn determinant af orden 4 ☞ [LA] 8 Determinanter Eksempel 1 1 0 7 0 0 1 0 0 0 0 1 0 = (−1) 0 0 0 1 4+4 1 0 7 0 1 0 0 0 1
V. Matricer – 4. Determinanter = (−1) 423 3+3 1 0 = 1 0 1 4.8. Trekantsmatrix ☞ [LA] 8 Determinanter Eksempler 0-række/søjle 0 a12 · · · 0 a22 · · · = . . . .. · · · 0 0 · · · a21 . a22 . .. · · · · · · = 0 Øvre trekantsmatrix a11 a12 · · · a1n 0 a22 · · · a2n . . . . . . .. . = a11a22 · · · ann . 0 0 · · · ann 4.9. Rækkeoperationsmatricer ☞ [LA] 8 Determinanter Observation
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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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I. Differentiation - 4. Kædereglen
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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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VI. Egenvektorer og diagonalisering
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VI. Egenvektorer og diagonalisering
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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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