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## Homework Statement

Consider matrices A = [1 2;2 4] and P = [1 3;3 6]. Using B = P^-1*A*P, verify that similar matrices have the same eigenvalues. Find the eigenvectors y for B and show that x = P*y are eigenvectors of A.

## Homework Equations

B = P^-1*A*P,

x = P*y

## The Attempt at a Solution

I have

P^-1 = [-2 1;1 -.333]

B = [0 0;2.333 4.999]

eigenvalues for matrices A and B are 0 and 5.

eigenvectors, y are

x2*[0 1]

x2*[-2.14 1]

eigenvectors for matrix A are

x2*[-2 1]

x2*[.5 1]

P*y = [1 3;3 6]*[0 1 ; -2.14 1]

I get x = [3 .86;6 -.42]

What am I doing wrong?