In my ODE class our professor has thrown a lot of stuff at us. There are only 2 people in my class at this small uni and it is hard for us to study or get much help from eachother.
This question seems more aligned with linear algebra though so I have posted in this section for some guidance. It has been a struggle.
Let f1, f2 and f3 be continuous functions on (a, b).
Set cij =integral from a to b of [fi(x)fj(x) dx]
Prove that these functions are linearly independent on (a, b) if and only if
c11 c12 c13
c21 c22 c23 /=0
c31 c32 c33
How can one extend this result to the case of n functions on (a, b)?
Thank you in advance