I'm trying to find out what geometric effect the following matrix $Ax$ where $x$ is a vector in the x y plane
has but it doesn't look like a transformation I'm normally accustomed too.
A=$\begin{pmatrix} 6 & 2 \\ 2 & 3 \end{pmatrix}$
If I try $A(1,0)$ I get $(6,2)$ and if I try $A(0,1)$ I get $(2,3)$ but I'm not sure what kind of transformation this is
The matrix has two eigenvalues 2 and 7. As it is a symmetric matrix, the two eigenspaces are mutually orthogonal. They are the straight lines $y = x/2$ and $y = -2x$. In the direction of the first straight line, vectors are multiplied by 7, in the direction of the second straight line, vectors are multiplied by 2.