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anonymous

  • 5 years ago

examine the following sets for linear independence: u1=eix, u2=e-ix, u3=sinx

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  1. nowhereman
    • 5 years ago
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    sorry, but those are no sets.

  2. anonymous
    • 5 years ago
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    \[u_{1}=e ^{ix}, u _{2}=e ^{-ix}, u _{3}=sinx\]

  3. nowhereman
    • 5 years ago
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    still those are only terms with the free variable x

  4. nowhereman
    • 5 years ago
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    do you mean \[\{e^{ix}, e^{-ix}, \sin{x}\}\] for an arbitrary x or do you mean \[\{e^{ix} | x \in ℂ \}\] and so on?

  5. anonymous
    • 5 years ago
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    an arbitrary

  6. anonymous
    • 5 years ago
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    \[c _{1}u _{1}+c _{2}u _{2}+c _{3}u _{3}\] if linear combination is zero c1, c2, c3=0 then its called linear independence.

  7. nowhereman
    • 5 years ago
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    they dependent: \[\sin x = \frac{e^{ix} - e^{x}}{2i}\]

  8. anonymous
    • 5 years ago
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    could you explain how this combination come?

  9. nowhereman
    • 5 years ago
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    It arises naturally if you define sinus and the exponential function by their power series. But also if you take geometric intuition and define \[e^{a+bi} = e^a(\cos b + i \sin b)\]

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