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Linear transformation questions.

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data

    See attached images below.

    2. Relevant equations

    For attachment "Linear 1," I've proven that it is indeed a linear transformation. My question is what does it mean when it says to show T^2=T? What exactly is the T that I am multiplying by itself?

    Attachment "Linear 2," I have found A to be [1 2|
    |2 5]
    How am I supposed to find the fA^-1 it asks for? Do I just take the inverse of the A I found?

    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 14, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Show if you apply T twice to a vector then you get the same result as applying it once. That's what T^2 means here. And sure, find the inverse of the matrix A and write out its action on a vector like they did with ##f_A##.
     
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