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Which of these transformations are linear?

  1. Apr 16, 2013 #1
    $$y_{1}=2x_{2}$$
    $$y_{2}=x_{2}+2$$
    $$y_{3}=2x_{2}$$

    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

    Mark44

    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

    Mark44

    Staff: Mentor

    Do you have enough information to start the problem now?
     
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