Find an invertible matrix P and a diagonal matrix D so that (P^−1)AP = D, where

A =

4 2

3 3

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- Jul 12th 2006, 04:18 PMluckyc1423diagonal matrix
Find an invertible matrix P and a diagonal matrix D so that (P^−1)AP = D, where

A =

4 2

3 3 - Jul 12th 2006, 06:39 PMgalactus
I'll start you off.

Find your charpoly:

The roots of this quadratic are your eigenvalues.

They are 1 and 6.

Sub them in for lambda in the matrix we derived, getting:

Use rref on these matrices and we find:

Your solutions are:

, respectively.

Bases for the eigenspace are:

Let this be P:

Now, find . You have all the necessary info.

Check me out. Easy to flub up.

I hope this helps.

If you don't have one, get a good linear algebra text. Anton and Rorres publish some good ones. - Jul 12th 2006, 07:39 PMluckyc1423
I am completely confused on this whole problem. If you could finish this off, then put an example for me to do and ill do it and post it to see if I got it right, thanks.

- Jul 13th 2006, 05:09 AMgalactus
I went ahead and made some changes. I hope you can finish up. The worst is done.

Good luck on your distance learning class. I know they can be a booger.

Try this one:

Find a matrix P that diagonalizes: