Science talk:Math Exam Resources/Courses/MATH221/April 2013/Question 08

Are not always zero for the eigenvalues 5 and -2. The P matrix should be something like

   0.7071   -0.6000         0
        0         0    1.0000
   0.7071    0.8000         0

According to MATLAB (the first column is likely sqrt(2)/2). This gives the diagonal matrix diag(5,-2,3).

I fixed the matrix computations and I think I verified them using Sage as well.