Consider 3 equal masses of mass m connected by equal springs with spring constant k, with masses 1 & 3 also connected to the walls by springs with constant k (diagram (c) from last week's homework, or Georgi 3.3 with all masses, springs the same). a) Write down the MK matrix (you did this last week). Write down S, the 3x3 reflection symmetry matrix. Show that M-KS=SM-K. b) What are the eigenvalues of S? Do not directly compute the eignevalues using the determinant for- mula, but instead use the fact that two mirror reflections is the same as the original. c) Find 3 eigenvectors of S. Show that the eigenvector with a unique eigenvalue is also an eigenvector of M-K. d) Unless you are very lucky in your initial guess, the two eigenvectors of S you found that have the same eigenvalue will not be eigenvectors of MK. Show that the two remaining eigenvectors of M-K you found last week are eigenvectors of S and show that these can be written as a linear combination of the eigenvectors you found already.