Recent content by Mitch_C

  1. M

    Show that a linear map is linearly independent

    Yeah I got that part too. I also see why it's a key part :)
  2. M

    Is V Isomorphic to R^2 Under the Given Mapping?

    Thanks for that. Looking back on it the basis I picked is obviously not a basis I just wasn't thinking. Spelling out for me what f(u) equals really helped. When I came back to it I solved it in about 10mins! Thanks again! :)
  3. M

    Show that a linear map is linearly independent

    Ok that's great thanks a lot! Not only do I now have the question done but I understand it all too! I'm a happy bunny :) So to make sure I did it right, I took fn the first time to show a0=0 and then fn-1 to show a1=0 and so on until you get fn-n which just gives you the equation back. And...
  4. M

    Show that a linear map is linearly independent

    Ok I think I get you. So how would I go about picking an m and p? Or can I prove that arbitrarily? and for the fb would that be so fb(v) = 1?
  5. M

    Is V Isomorphic to R^2 Under the Given Mapping?

    Homework Statement Let V={a cosx + b sinx | a,b \in R} (a) Show that V is a subspace of the R-vector space of all maps from R to R. (b) Show that V is isomorphic to R^2, under the map f: V\rightarrowR^2 a cosx + b sinx \rightleftharpoons [ a over b ] (this is...
  6. M

    Show that a linear map is linearly independent

    Homework Statement Let f:V\rightarrow V be a linear map and let v\inV be such that f^n(v)\neq0 and f^(n+1)(v)=0. Show that v,f(v),...,f^(n-1)(v) are linearly independent. The Attempt at a Solution I'm really stuck with this one. I know the definition of linear independence and...