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VI. Egenvektorer og diagonalisering – 1. Egenvektorer 448 For λ1 = 0 er koefficientmatricen ⎛ 1 0 ⎞ 1 ⎛ 1 0 ⎞ 1 A = ⎝0 1 1⎠ ∼ ⎝0 1 1⎠ 2 −1 1 0 0 0 Egenvektorerne er da løsninger til det reducerede ligningssystem hvor x3 er en fri variabel. x1 + x3 = 0 x2 + x3 = 0 1.26. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 3, 4 - fortsat Dette giver Heraf fås egenvektorerne ⎛ hvor x3 vælges frit. ⎝ x1 x2 x3 x1 = −x3 x2 = −x3 ⎞ ⎛ ⎞ ⎛ ⎞ −x3 −1 ⎠ = ⎝−x3⎠ = x3 ⎝−1⎠ 1 x3 1.27. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 3, 4 - fortsat
VI. Egenvektorer og diagonalisering – 1. Egenvektorer 449 For λ2 = 1 er koefficientmatricen ⎛ 0 A − I = ⎝0 0 0 ⎞ ⎛ 1 1 1⎠ ∼ ⎝0 −1 2 0 ⎞ 0 1⎠ 2 −1 0 0 0 0 Egenvektorerne er da løsninger til det reducerede ligningssystem hvor x2 er en fri variabel. x1 − 1 2 x2 = 0 x3 = 0 1.28. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 3, 4 - fortsat Dette giver x1 = 1 2 x2 x3 = 0 Heraf fås egenvektorerne ⎛ hvor x2 vælges frit. ⎝ x1 x2 x3 ⎞ ⎛ ⎠ = ⎝ 1 2x2 x2 0 ⎞ ⎛ 1 2 ⎞ ⎠ = x2 ⎝1⎠ 0 1.29. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 3, 4 - 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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