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V. Matricer – 2. Lineære afbildninger 396 Notation Givet ligningssystemet (1) A koefficientmatrix (2) b = 0 homogent system (3) b = 0 inhomogent system Ax = b (4) Partikulær løsning en funden løsning, fuldstændig løsning mængden af alle løsninger 2.21. 2 ligninger 3 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel 1 2x1 − 2x2 − 4x3 = −28 x2 + 2x3 = 16 (1) Vælg x3 = 0 og løs x2 = 16. Indsæt i første ligning (2) Dette giver partikulær løsning 2x1 − 2 · 16 = −28 (x1,x2,x3) = (2,16,0) 2.22. 2 ligninger 3 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel 1 - fortsat
V. Matricer – 2. Lineære afbildninger 397 Den fuldstændige løsning er ⎛ ⎞ ⎝ hvor x3 kan vælges frit. x1 x2 x3 ⎠ = = ⎛ ⎞ ⎛ ⎞ x2 + 2x3 − 14 2 ⎝ −2x3 + 16 ⎠ = ⎝−2x3 + 16⎠ x3 x3 ⎛ ⎞ 2 ⎛ 0 ⎞ ⎛ ⎞ 2 ⎛ ⎞ 0 ⎝16⎠ + ⎝−2x3⎠ = ⎝16⎠ + x3 ⎝−2⎠ 0 0 1 x3 2.23. 1 ligning 3 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel 1’ x1 + x2 + x3 = 1 (1) Vælg x3 = x2 = 0 og løs x1 = 1 (2) Det giver partikulær løsning (x1,x2,x3) = (1,0,0) 2.24. 1 ligning 3 ubkendte ☞ [LA] 5 Lineære ligningssystemer Eksempel 1’ - fortsat
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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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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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