So I am given B=\begin{array}{cc} 3 & 5 \\ 5 & 3 \end{array}. I find the eigenvalues and eigenvectors: 8, -2, and (1, 1), (1, -1), respectively. I am then told to form the matrix of normalised eigenvectors, S, and I do, then to find S^{-1}BS, which, with S = \frac{1}{\sqrt{2}}\begin{array}{cc} 1...