Math Help - Calculating eigenvectors

1. Calculating eigenvectors

Find the eigenvalues and eigenvectors of $A = \left(\begin{array}{cc}1&3\\3&1\end{array}\right)$.

I have found the eigenvalues for this problem being $\lambda1 = 0$ and $\lambda2 = 2$.

My problem is i'm having trouble working out the corrosponding eigenvectors.

2. To find the eigenvectors, one must find find a basis for the null space. Fortunately, in your case it is really easy because you have distinct eigenvalues, so you only need to find vectors $\vec{v_i}$ that satisfy $(A-\lambda_i I_2)\vec{v_i}=\vec{0}$.

In layman's terms subtract your eigenvalues from the diagonal and solve the rsystem of equation for x and y when it is set equal to zero.

$\lambda_1=0$
I get $v_1=<-3,1>$

$\lambda_2=2$
I get $v_1=<3,1>$

3. Originally Posted by chuckienz
Find the eigenvalues and eigenvectors of $A = \left(\begin{array}{cc}1&3\\3&1\end{array}\right)$.

I have found the eigenvalues for this problem being $\lambda1 = 0$ and $\lambda2 = 2$. Not correct!

My problem is i'm having trouble working out the corresponding eigenvectors.
In fact, the eigenvalues of that matrix are 4 and –2.

4. I had a sneaking suspicion I should have checked the work before doing mine, lol. Good catch.