I am given the question: Let I be an interval and let y1, . . . , yM be vector functions I - C^N. Show that if t0 € I and y1(t), . . . , yM(t) € C^N are linearly independent vectors then y1,....,ym are linearly independent functions.
Argue by contradiction. Thus assume the
M functions y1(t), . . . , yM(t) are linearly dependent i.e.that there exist constants c1, . . . , cM not all zero such that
cjyj(t) = 0 for all t € I. I want to evaluate at t=t0 but I'm not sure what to do next.
Any suggestions would be awesome