In order to get a better understanding of Eigenvectors and Eigenvalues, I am plotting both the given and calculated the vectors geometrically using Graphics[] and running into problems - see attached notebook.

1. The calculated eigenvectors seem to have a different magnitude than the original vectors, which I am assuming is the result of me not including the Eigenvalues in the graph. However, when I try to include the calculated Eigenvalues into the graph, I get error messages, which are probably syntax errors resulting in me not coding the function correctly. So would someone please show me the correct way to include the Eigenvalues into the Graphic function?

2. It appears that the calculated eigenvectors point in a different direction than the given vectors, which I do not understand. So, would someone with a better understanding of Eigenvectors help me get a better understanding as to what the geometric view is actual showing me?

Thanks,
Mitch Sandlin