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V. Matricer – 1. Vektorer og matricer 380 Associativ lov Distributive love A + (B + C) = (A + B) + C A(B + C) = AB + AC (A + B)C = AC + BC 1.25. Pas på Advarsler Den kommutative lov holder ikke Normalt er ☞ [LA] 2 Matricer 0 AB = BA 0 0 0 0 = 0 Nulreglen gœlder ikke 1 0 0 1 0 0 0 0 = 0 1 1 0 0 0 0 0 1 0 A = 0, B = 0, AB = 0 1.26. Test matrix multiplikation ☞ [LA] 2 Matricer Test
V. Matricer – 1. Vektorer og matricer 381 Hvilket matrixprodukt er rigtigt? 2 1 x 1 2 1 + x 2 + 4x (a) = . 3 4 x 4 3 + 4x 22 1 2 1 −2 7 6 (b) = . 3 4 3 4 15 12 Løsning 1 x 1 2 = 3 4 x 4 [1 · 1 + x · x] [1 · 2 + x · 4] . [3 · 1 + 4 · x] [2 · 3 + 4 · 4] Afkryds det rigtige: (a) (b) 1.27. Enhedsvektorer Eksempel ☞ [LA] 3 Lineære funktioner Den i-te standard enhedsvektor ei er (søjle,række)-vektoren, hvis i-te koordinat er 1 og alle øvrige er 0. ⎛ ⎞ 0 ⎜ . ⎜ . ⎟ ⎜ . ⎟ ei = ⎜ ⎜1 ⎟ ⎜ . ⎟ ⎝ . ⎠ 0 ei = 0, ..., 1, ..., 0
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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 - 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. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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VII. Skalarprodukt og projektion -
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VIII. Appendiks - 1. Polære koordi
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IX. Opgaver - 1. August 2002 524 1.
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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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