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December 4th, 2010, 07:05 AM   #1
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Eigenvalues/Vectors and Invertible Matrices

Hi guys! I've been given a few Eigenvalues/Vectors problem as introduction to the topic. I've figured out rather easily how to find the eigenvalues/vectors of a 2x2 and 3x3 matrix, but I have no idea how to approach this problem! It's likely linked somehow...



If anyone could steer me on the right path it would be so appreciated!

This problem is then followed up by this one:



Which is the same matrix, but I'm not sure what they're asking for. Any ideas?

Thanks,
Steel.
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December 4th, 2010, 10:26 AM   #2
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Re: Eigenvalues/Vectors and Invertible Matrices

2a)

If P=
[[1 3 2]
[0 -4 -5]
[1 1 2]]
then
P^-1AP=
[[-3 0 0]
[0 5 0]
[0 0 7]]

Eigenvalues of A: -3, 5, 7
Eigenvectors of A: [1, 0, 1], [3, -4, 1], [2, -5, 2].
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December 4th, 2010, 03:20 PM   #3
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Re: Eigenvalues/Vectors and Invertible Matrices

I see how using eigenvectors...this was easier than I thought.

Thank you very much!
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