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V. Matricer – 3. Lineære ligninger 408 2x1 − 2x2 − 4x3 − 6x4 = −16 x2 + 2x3 + 6x4 = 4 − 3x4 = 6 3.12. Afslut bagfra ☞ [LA] 6 Løsningsteknik Eksempel’ - fortsat Heraf 2x1 − 2x2 − 4x3 − 6x4 = −16 x2 + 2x3 + 6x4 = 4 − 3x4 = 6 x4 = −2 x2 = 4 − 2x3 − 6x4 = 16 − 2x3 x1 = −8 + x2 + 2x3 + 3x4 = 2 3.13. En fri tre bundne ☞ [LA] 6 Løsningsteknik Eksempel’ - fortsat Løsning x4 = −2 x2 = 16 − 2x3 x1 = 2
V. Matricer – 3. Lineære ligninger 409 På matrix form ⎛ ⎜ ⎝ x1 x2 x3 x4 ⎞ ⎟ ⎠ = ⎛ ⎞ 2 ⎜ ⎜16 − 2x3 ⎟ ⎝ ⎠ = ⎛ ⎞ 2 ⎜ ⎜16 ⎟ ⎝ 0 ⎠ −2 x3 −2 + x3 ⎛ ⎞ 0 ⎜ ⎜−2 ⎟ ⎝ 1 ⎠ 0 3.14. Rækkeoperationer reduceret matrix ☞ [LA] 6 Løsningsteknik Definition Rœkkeoperationer på en matrix • Ombytning af to rækker • Multiplikation af række med tal = 0 • Addition af et multiplum af en række til en anden Bringer matricen på (reduceret) rœkke-echelon form (trappeform), 1 på pivot indgange ⎛ ⎞ 0 0 1 ? ? 0 ? ? 0 ⎜ 0 0 0 0 0 1 ? ? 0 ⎟ ⎝ 0 0 0 0 0 0 0 0 1 ⎠ 0 0 0 0 0 0 0 0 0 3.15. Strategi på matrix form ☞ [LA] 6 Løsningsteknik 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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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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