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#1 2008-05-27 02:52:28
- missbossyy
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- Registered: 2008-02-01
- Posts: 38
Differential eqs
Observe that for the functions f1(x) =2 and f2 (x) = ex ,
1. f1(0) - 2. f2(0) = 0
Does this imply that f1 and f2 are linearly dependent on any interval containing x=0?
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#2 2008-05-27 03:36:26
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Differential eqs
The Wronskian is
[Dickinson]\left|\begin{array}{rr}2&\mathrm{e}x\\0&\mathrm{e}\end{array}\right|\ =\ 2\mathrm{e}\ \ne\ 0[/Dickinson]
Hence the two functions are linearly independent on any interval.
Note: The linear dependence/independence of functions has nothing to do with particular values of the functions themselves. The fact that f[sub]2[/sub] vanishes at x = 0 is immaterial the important thing is that f[sub]2[/sub] itself is not the zero function.
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