Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Mathematics 3C, Fall 2011 Selected Solutions to Worksheet 4, TA Grace Kennedy
 

Summary: Mathematics 3C, Fall 2011
Selected Solutions to Worksheet 4, TA Grace Kennedy
NAME:
MY WEBSITE: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
4. Is the following set of functions in C[0, 1] linearly independent?
S = {cos(t), cos(2t), cos(3t)}
Intuitively, when you try to apply the definition of linear independence: do
there exist nontrivial a, b, c R so that a cos(t) + b cos(2t) + c cos(3t) = 0,
you should think `it would be weird if you could scale trig functions so that they
cancel out with scalars on the inside...' Scaling trig functions on the outside
changes the altitude while scaling them on the inside changes their period, or
how close together the humps are, but not the height.
The rigourous way to show this is by using the Wronskian, which you learned
in lecture on Thursday the 27th, but this problem would be tedious with that
method. I intended this to be approached intuitively.
5. Is the following set of functions in C[0, 1] linearly independent?
S = cos(

2

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics