# Eigenvalues

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• Feb 16th 2010, 05:09 PM
steph3824
Eigenvalues
Hi everyone, I am needing some help. I have the matrix

A= [2 1/2]
.....[-1/2 1]

According to my book, the eigenvalue for this is λ1= λ2=3/2 and the eigenvector is
v=[1]
...[-1]

However, this is not what I am getting. I'm not seeing where they are getting the 3/2 from. I know the process of finding the eigenvalue because I have successfully solved my other homework problems but this one is stumping me. Can someone show how to get the 3/2 eigenvalue?
• Feb 16th 2010, 05:19 PM
pickslides
by $\det(A-\lambda I)=0$

you get the quadratic

$\lambda^2-3\lambda+ \frac{9}{4}=0$

which factors to be

$\left(\lambda-\frac{3}{2}\right)^2=0$

gives $\lambda = \frac{3}{2}$
• Feb 16th 2010, 05:44 PM
steph3824
OH ok I see it...I must have been havin a brain fart. Thanks for your help!