In the eigenvector calculation, for the eigenvalue -0.5, how do the solutions deduce that x1 = -3/4? The way I had learnt to calculate eigenvectors would have given me the eigenvector (1,1,-4/3) transposed. Am I missing something important?
Yeah I got the same, but they're essentially the same answer. Your eigenvector is just a scalar mutiple of the eigenvector in the solutions i.e. (-3/4,-3/4,1)*-4/3 = (1,1,-4/3) You need to normalise the eigenvectors to use for the "Eigenvalue Method" which should bring your answer in line with solutions. You might get the -ve of the one in the solutions but it'll cancel out in the final step and give the same answer.
