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Homework Help: Linear Algebra - Linear transformation quesiton

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data

    The linear operator T on R2 has the matrix
    [tex]
    \begin{bmatrix}4 & -1\\-4 & 3 \end{bmatrix}
    [/tex] relative to the basis A = B = {(1,2), (0, 1)}. A vector u has coordinates [tex]


    \begin{bmatrix}1 \\1\end{bmatrix}

    [/tex] relative to this basis. Find T(u) in component form (x, y)

    2. Relevant equations



    3. The attempt at a solution

    I apply T to u = [tex]
    \begin{bmatrix}4 & -1\\-4 & 3 \end{bmatrix} \begin{bmatrix}1 \\1\end{bmatrix} = \begin{bmatrix} 3 \\-1\end{bmatrix} [/tex]

    = relative to the given basis

    Then T(u) = {(3,6), (0,-1)}

    Does that look right?
     
  2. jcsd
  3. Feb 4, 2010 #2
    Your answer is in the wrong form.

    [tex] \begin{bmatrix} 3 \\-1 \end{bmatrix} = 3 \begin{bmatrix} 1 \\0 \end{bmatrix} + (-1) \begin{bmatrix} 0 \\1 \end{bmatrix} = 3 (1,2) + (-1) (0,1)[/tex]
     
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