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V. Matricer – 2. Lineære afbildninger 400 2.28. Løsninger og nulrum ☞ [LA] 5 Lineære ligningssystemer Sætning 8 Givet en partikulœr løsning u til det lineœre ligningssystem med n ubekendte så er løsningsmœngden Ax = b {x ∈ R n |Ax = b} = u + NA Bevis Simple regneregler for matrix multiplikationen giver Au = b, Ax = 0 ⇒ A(u + x) = b 2.29. Test Løsningsmængde Test ☞ [LA] 5 Lineære ligningssystemer Betragt et inhomogent lineært ligningssystem A·x = b (b = 0). Hvilket af følgende udsagn er sandt (uanset hvordan A ser ud) (a) 0 er altid en løsning. (c) b er altid en løsning. (b) 0 er aldrig en løsning. Afkryds det sande: (a) (b) (c)
V. Matricer – 2. Lineære afbildninger 401 Løsning Gør prøve A · 0 = 0 = b 2.30. 2 ligninger 4 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel x1 + x2 = 1 x3 + x4 = 2 (1) x3 = 2, x1 = 1 og x2 = x4 = 0 (2) Giver en partikulær løsning x4 (x1,x2,x3,x4) = (1,0,2,0) 2.31. 2 ligninger 4 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel - fortsat ⎛ ⎞ x1 ⎜x2⎟ ⎜ ⎟ ⎝x3⎠ = ⎛ ⎞ 1 − x2 ⎜ x2 ⎟ ⎜ ⎟ ⎝2 − x4⎠ = ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 1 −1 0 ⎜ ⎜0⎟ ⎜ ⎟ ⎝2⎠ + x2 ⎜ 1 ⎟ ⎜ ⎟ ⎝ 0 ⎠ + x4 ⎜ 0 ⎟ ⎝−1⎠ 0 0 1 x4
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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 - 2. Partielle a
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I. Differentiation - 7. Lagrangemet
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1. Grafiske/numeriske metoder IV Di
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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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