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V. Matricer – 4. Determinanter 430 Test Givet en kvadratisk matrix A. Hvis det(A 2 ) = 0, så er det(A) = 0. Løsning Af produktreglen følger det(A) 2 = det(A 2 ) = 0 Afkryds: ja nej 4.22. Determinant af negative potenser ☞ [LA] 8 Determinanter Eksempel Negative potensers determinant −1 2 3 4 = (−1) · 4 − 2 · 3 = −10 −1 −1 2 = − 3 4 1 10 −k −1 2 = 3 4 1 (−10) k
V. Matricer – 4. Determinanter 431 4.23. Determinant af alle potenser ☞ [LA] 8 Determinanter Eksempel Potensreglen for determinant • Hvis |A| = 0 så for alle hele tal k. • Hvis |A| = 0 så for alle hele tal k > 0. |A k | = |A| k |A k | = 0 4.24. Jacobimatricen ☞ [LA] 2.2 Kædereglen i matrix-formulering Definition For en differentiabel afbildning g : R n → R n (u1,...,un) ↦→ (g1(u1,...,un),...,gn(u1,...,un)) er Jacobideterminanten determinanten af Jacobimatricen ∂g1 ... ∂u1 |du(g)| = . . . .. ∂gn ... ∂u1 . . ∂g1 ∂un ∂gn ∂un
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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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