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Homework Help: Identify all linear transformations from C2 to C3

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    WjnxU.jpg

    2. Relevant equations



    3. The attempt at a solution

    In the previous problem I was asked to identify if a polynomial, such as f(x)=2x was a linear transformation. In that case I checked to see if f(ax + by) = f(ax) + f(by). I figure I would be doing something similar in this case.

    I would check to see if T(ax + by) = T(ax) + T(by).

    So for problem (A) would I do something like:

    5zU9J.jpg

    and since T(ax + by) ≠ T(ax) + T(by), T1 is not a linear transformation?
     
  2. jcsd
  3. Oct 9, 2011 #2
    You are correct, T1 is not a linear transformation, and your argument is correct/valid.
     
  4. Oct 9, 2011 #3
    Thanks!
     
  5. Oct 9, 2011 #4
    I have a question about part (D), which is

    [tex]

    Tx =
    \left[ {\begin{array}{cc}
    1 & 0 \\
    2-i & 3i \\
    i-i & 4\\
    \end{array} } \right]x
    [/tex]

    I assume I use the same procedure? Is anything special I need to do in regards to the complex variables?

    I find that it IS a linear transformation, is that correct? Also, isn't i-i just 0?
     
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