2 Attachment(s)

Issue with Eigenvectors [solved]

I put my problem in the pdf document since matrices are tedious in latex...I am trying to find eigenvectors for a linear system, I can produce the same eigenvalues given by wolfram (see pic of wolfram results)...but I cannot get the same eigenvectors and I cannot resolve the problem...or figure out what's wrong...

The pdf is the problem...the pic is the wolfram results...

Re: Issue with Eigenvectors

Ok, nevermind, I see what the problem is now. The equations are just redundant, and it means that there are infinitely many eigenvectors such that any x I chose will correspond to a y value given by one of the equations. (Rock)(Rock)(Rock)

Re: Issue with Eigenvectors [solved]

You are looking for a vector $\displaystyle \begin{pmatrix}x \\ y\end{pmatrix}$ such that $\displaystyle \begin{pmatrix}1&1 \\ 1&0\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix} = \lambda \begin{pmatrix}x \\ y\end{pmatrix}$

So, you found your eigenvalues. Now, solve for the vector. Figure out the matrix multiplication, figure out the scalar multiplication, then solve for your $\displaystyle x$ and $\displaystyle y$. There should be an infinite number of solutions (the Eigenspace). Choose a non-zero solution.