Find, if possible, a nonsingular matrix P such that is diagonal.

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- Apr 20th 2009, 07:04 AMjennifer1004How to find nonsingular matrix?
Find, if possible, a nonsingular matrix P such that is diagonal.

- Apr 20th 2009, 07:24 AMTheEmptySet
First you need to find the eigenvalues so you can find the eigen Basis for the matrix (if it exists)

Expanding along the first column we get

So the two eigenvalues are

Using we get the matrix

Reducing we get

This implies that there are two parameters in the solution so let

so the last equation is

so the solution is

So these are the first two eigenvectors

Now using the eigen values we get

Reducing we get

This has 1 parameter in its solution so let

We can see that and

So the solution is

The eigenvectors are the columns of the matrix P. - Apr 21st 2009, 02:24 PMjennifer1004
so my answer is simply ?

Thank you for showing your work. It has helped me so much. I can now use your example to help me figure out problems on my own. - Apr 21st 2009, 02:28 PMTheEmptySet
- Apr 21st 2009, 04:46 PMjennifer1004
Out of curiosity, you wouldn't multiply the eigenvector for by 3 for the final matrix, which would make it ?