1. (35 pts.) Consider the following matrix: 2 1 2 4 1 4 0 (a) Find the eigenvalues and eigenvectors using MATLAB. (b) Use MATLAB to demonstrate that the eigenvectors form an or- thonormal set of vectors. (c) Compute the Rayleigh Quotient to demonstrate the solution is cor- rect. (d) Recall that the eigenvectors of a symmetric matrix form an orthonor- mal coordinate system. Given the vector X= in the coordinate system defined by the eigenvectors, find its compo- ments in the original coordinate system