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V. Matricer – 2. Lineære afbildninger 394 og k = 0,1,2,... er potensen Λ k = ⎛ ⎜ ⎝ λ k 1 0 ... 0 . .. 0 . 0 λ k n 2.17. Matrix potens ☞ [LA] 2 Matricer Opgave Beregn matrix potensen 1 k a 0 1 Løsning Bemærk 1 0 x 1 1 0 y 1 = 1 0 x + y 1 Heraf 1 0 k a 1 = 1 0 ka 1 2.18. Ligninger på matrix form ☞ [LA] 5 Lineære ligningssystemer Definition ⎞ ⎟ ⎠
V. Matricer – 2. Lineære afbildninger 395 Ved m lineære ligninger med n ubekendte forstås a11x1 + ... + a1nxn = b1 a21x1 + ... + a2nxn = b2 . am1x1 + ... + amnxn = bm På matrix form A = (aij) m × n-matrix, b = (bi) m-søjle, x = (xj) n-søjle Ax = b 2.19. Ligninger på matrix form ☞ [LA] 5 Lineære ligningssystemer Definition - fortsat Matrix form Ax = b skrevet ud ⎛ a11 ... a1n ⎜a21 ⎜ ... a2n ⎜ . ⎝ . am1 ... amn ⎞ ⎛ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ x1 x2 . xn ⎞ ⎛ b1 ⎟ ⎠ = ⎜b2 ⎜ . ⎝ . 2.20. Koefficient matrix ☞ [LA] 5 Lineære ligningssystemer bm ⎞ ⎟ ⎠
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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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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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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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