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anonymous
 5 years ago
examine the following sets for linear independence: u1=eix, u2=eix, u3=sinx
anonymous
 5 years ago
examine the following sets for linear independence: u1=eix, u2=eix, u3=sinx

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nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, but those are no sets.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[u_{1}=e ^{ix}, u _{2}=e ^{ix}, u _{3}=sinx\]

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0still those are only terms with the free variable x

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0do you mean \[\{e^{ix}, e^{ix}, \sin{x}\}\] for an arbitrary x or do you mean \[\{e^{ix}  x \in ℂ \}\] and so on?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[c _{1}u _{1}+c _{2}u _{2}+c _{3}u _{3}\] if linear combination is zero c1, c2, c3=0 then its called linear independence.

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0they dependent: \[\sin x = \frac{e^{ix}  e^{x}}{2i}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could you explain how this combination come?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0It 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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