Hey there,

So I've been given this question, determine a matrix P so that P^-1AP=B?

The questions relate to the matrices

A = [1 2 3]

[0 -1 2]

[0 0 3]

B= [-1 -2 3]

[0 1 -5]

[0 0 3]

The eigenvalues for the matrices are the same: lamda equals 3, 1 and -1.

And the eigenvectors for lamda equals 1 and -1 are the same for both matrices: for 1: 1, 0, 0 and for -1: -1, 1, 0.

The eigenvectors for lamda equals 3 in A: 2, 1/2, 1.

The eigenvectors for lamda equals 3 in B: 2, -5/2, 1.

So I've done a lot of working out so far but now I'm stuck! Can anyone let me know how to go about finding matrix P.

I thought I was just meant to put the eigenvectors of A into a matrix:

e.g. [1 -1 2]

[0 1 1/2]

[0 0 1]

However, that didn't work so I'm really unsure now!

Thanks heaps in advance.