Dimension of subspace

  • Thread starter Dustinsfl
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  • #1
Dustinsfl
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C[-pi, pi]
Span(1, cos (2x), cos2 (x))

Doing the Wronskian here is pain so what other method would be more appropriate?
 
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Answers and Replies

  • #2
36,312
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One of the functions is a linear combination of the other two, so the three functions can't be linearly independent.
 
  • #3
Dustinsfl
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How can I go about identifying if one is?
 
  • #4
VeeEight
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Use a trig identity for cos2x
 
  • #5
Dustinsfl
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cos2x=2cos^2 x-1 but I don't see how that is a multiple of cos2x sine it doesn't = cos^2 x outright.
 
  • #6
VeeEight
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Can cos2x can be written as a linear combination of cos2x and 1?
 
  • #7
Dustinsfl
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I see now.
 
  • #8
VeeEight
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Great :smile:
 
  • #9
36,312
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cos2x=2cos^2 x-1 but I don't see how that is a multiple of cos2x sine it doesn't = cos^2 x outright.
I realize that you already figured this out, but if you look at what I said, I didn't say that one of the functions was a multiple of another. I said that one function was a linear combination of the other two.
 

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