• Support PF! Buy your school textbooks, materials and every day products Here!

Dimension of subspace

  • Thread starter Dustinsfl
  • Start date
  • #1
699
5
C[-pi, pi]
Span(1, cos (2x), cos2 (x))

Doing the Wronskian here is pain so what other method would be more appropriate?
 
Last edited:

Answers and Replies

  • #2
33,496
5,188
One of the functions is a linear combination of the other two, so the three functions can't be linearly independent.
 
  • #3
699
5
How can I go about identifying if one is?
 
  • #4
614
0
Use a trig identity for cos2x
 
  • #5
699
5
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
614
0
Can cos2x can be written as a linear combination of cos2x and 1?
 
  • #7
699
5
I see now.
 
  • #8
614
0
Great :smile:
 
  • #9
33,496
5,188
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.
 

Related Threads on Dimension of subspace

  • Last Post
Replies
24
Views
8K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
2K
Replies
2
Views
4K
  • Last Post
Replies
1
Views
913
Replies
2
Views
5K
Replies
2
Views
2K
Replies
6
Views
1K
  • Last Post
Replies
1
Views
2K
Top