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V. Matricer – 3. Lineære ligninger 414 3.23. Test ligningssystem Test ☞ [LA] 6 Løsningsteknik Et homogent lineært ligningssystem med 4 ubekendte og 3 ligninger har: (a) Altid højst 1 løsning. (b) Altid uendelig mange løsninger. (c) Undertiden ingen løsninger. (d) Mindst 1 løsning. Afkryds de to rigtige: (a) (b) (c) (d) Løsning Sætning 9 sikrer uendelig mange løsninger. 3.24. En sjov variation ☞ [LA] 6 Løsningsteknik Eksempel 4 Løs matrixligningen 2 1 5 3 Skrives som ligningssystemet x11 x12 x21 x22 = 1 0 0 1 2x11 + x21 = 1 5x11 + 3x21 = 0 2x12 + x22 = 0 5x12 + 3x22 = 1 3.25. Det er rigtig sjovt ☞ [LA] 6 Løsningsteknik
V. Matricer – 3. Lineære ligninger 415 ∼ ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ 2 1 0 0 1 5 3 0 0 0 0 0 2 1 0 0 0 5 3 1 1 0 0 0 3 0 1 0 0 −5 0 0 1 0 −1 0 0 0 1 2 ⎞ ⎟ ⎠ ∼ ⎞ ⎟ ⎠ , ⎛ ⎜ ⎝ 1 1 1 0 1 2 0 0 2 2 0 0 −5 2 1 0 0 1 2 0 1 0 0 0 2 1 x11 x12 x21 x22 = ⎞ ⎟ ⎠ 3 −1 −5 2 3.26. Operationer og multiplikation ☞ [LA] 7 Rækkeoperations-matricer Sætning Rœkkeoperationer på en m × n-matrix fremkommer ved • Udfør rœkkeoperationen på m × m-enhedsmatricen og få en rækkeoperationsmatrix • Venstre multiplicer den oprindelige matrix med den fremkomne rækkeoperationsmatrix 3.27. Smart overbevisende ☞ [LA] 7 Rækkeoperations-matricer • Ombytning af to rækker 0 1 1 0 a11 a12 a21 a22 = a21 a22 a11 a12
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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