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Math Help - martices problem

  1. #1
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    Aug 2008
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    martices problem

    this is the only problem i had in today's lecture, someone please help me..

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  2. #2
    Junior Member
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    Aug 2008
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    anyone can help me, please
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  3. #3
    Member
    Joined
    Aug 2008
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    Hello,

    Do you know how to get the matrix A associated to a linear transformation f?
    All you have to do is compute where the vectors e_1=\begin{pmatrix}1\\0\end{pmatrix} and e_2=\begin{pmatrix}0\\1\end{pmatrix} go.
    For example, if f(e_1)=\begin{pmatrix}1\\3\end{pmatrix} and f(e_2)=\begin{pmatrix}2\\4\end{pmatrix}, then the matrix A associated to f is A=\begin{pmatrix}1&2\\3&4\end{pmatrix}.

    Now, f_{\theta}(e_1)=\begin{pmatrix}\cos\theta\\\sin\th  eta\end{pmatrix}, f_{\theta}(e_2)=\begin{pmatrix}-\sin\theta\\\cos\theta\end{pmatrix}, g(e_1)=-e_1 and g(e_2)=e_2 will do.

    Bye.
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