A= 1 0 0 0 0 1 5 -10 1 0 2 0 1 0 0 903 (a) Find all the eigenvalues and eigenvectors of A. Write them down in pairs without normalization, for example, the first pair of eigenvalue and eigenvector is: 0 (A1, vi) = (1, - 2 0 2 1 - 0 t). 0 0 (b) Sanity check. Verify all the eigenvectors you just found. Let all the free vari- ables equal to 2. For the first pair, 1000 0 1 5 -10 1 0 2 0 1 0 0 3 2 Ar ; 11 = . 2 4 2 2