1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Which of these transformations are linear?

  1. Apr 16, 2013 #1

    I know that in order for a transformation to be linear it has to satisfy:

    I) $$T(v + w) = T(v) + T(w)$$
    II) $$T(kv) = kT(v)$$

    But what are v and w in this case?

    note: v and w are vectors and are suppose to have arrows on top of them but I was too lazy to figure out how to type this out :P
  2. jcsd
  3. Apr 16, 2013 #2


    Staff: Mentor

    v and w are vectors in the domain of the transformation. Presumably they would look like this:
    $$ v = \begin{bmatrix} v_1 \\ v_2\end{bmatrix}$$
    $$ w = \begin{bmatrix} w_1 \\ w_2\end{bmatrix}$$

    Is there information in the problem you haven't provided? When you post a problem, you need to provide the complete problem statement. Also, the three parts of the template are there for a reason - don't just delete them.
  4. Apr 17, 2013 #3

    Sorry about the formatting. I'll keep that in mind the next time I post. However, I did not leave out any parts of the problem. The problem simply asked which of these transformations are linear and then provided the 3 equations given.
  5. Apr 17, 2013 #4


    Staff: Mentor

    Do you have enough information to start the problem now?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted