# Thread: martices problem

1. ## martices problem

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

2. anyone can help me, please

3. 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.