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Homework Help: Linear Transormation?

  1. Nov 16, 2008 #1
    Linear Transormation???

    1. The problem statement, all variables and given/known data

    Is function T a linear transformation for T: M22 --> R by

    T [a b]
    [c d] ( i.e. T [a b ; c d] )= a + b + c + d

    2. Relevant equations


    T ( u + v) = T(u) + T(v)

    T(ru) = rT(u)


    3. The attempt at a solution

    The matrix form is confusing me
     
  2. jcsd
  3. Nov 16, 2008 #2
    Re: Linear Transormation???

    Let U be the matrix you defined and let r be an arbitrary scalar. You know how to calculate rU and you have the formula for calculating T(U), so does T(rU) = rT(U)?

    For the next part, define another matrix similarily as you did except with different letters. Call it V. Does T(U + V) = T(U) + T(V)?
     
  4. Nov 16, 2008 #3
    Re: Linear Transormation???

    the first part T(rU) = rT(U) satisfies
     
  5. Nov 16, 2008 #4
    Re: Linear Transormation???

    and i so does the second part! Am I right?
     
  6. Nov 16, 2008 #5
    Re: Linear Transormation???

    If you can show it then you are done.
     
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