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Thread: martices problem

  1. #1
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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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    anyone can help me, please
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  3. #3
    Member
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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 $\displaystyle e_1=\begin{pmatrix}1\\0\end{pmatrix}$ and $\displaystyle e_2=\begin{pmatrix}0\\1\end{pmatrix}$ go.
    For example, if $\displaystyle f(e_1)=\begin{pmatrix}1\\3\end{pmatrix}$ and $\displaystyle f(e_2)=\begin{pmatrix}2\\4\end{pmatrix}$, then the matrix A associated to f is $\displaystyle A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$.

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

    Bye.
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