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Homework Help: Matrix proof

  1. Oct 29, 2012 #1
    Define T: Mn×n → Mn×n by T (A) = At . Show
    that R(T) = Mn×n.

    Alright then. The transformation is saying that it's transforming an nxn matrix into an nxn matrix (duh).

    T(A)=A^t thus A^t is still an nxn matrix.

    Thus R(T) is all of Mnxn?


    Is that it?
     
  2. jcsd
  3. Oct 29, 2012 #2
    Also another part of the question is:
    Define T: Mn×n → Mn×n by T (A) = A − A^t .
    a. Find R(T ).
    b. Find N(T ).


    a) R(T) is just the right hand side (A-A^t) which is the set of all skew symmetric matrices?

    b) To find N(T) I set the RHS equal to 0. so A-A^t=0 thus A=A^t
    so N(T) is the set of all symmetric matrices?
     
  4. Oct 29, 2012 #3

    Dick

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    Yes for both. You seem to have a pretty good idea what you are doing. You might not need to post ALL of these questions.
     
  5. Oct 29, 2012 #4
    I'm insecure about most of my answers, even if a lot of them are right.
     
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