(a) Find the eigenvalues (A1 and A2) and eigenvectors (e and e2) of the following matrix: [83] A = (b) Verify that the product of your eigenvalues is the determinant of the matrix. (c) Verify that the sum of your eigenvalues is the trace of the matrix. (d) Verify that Ae;= Ae; for i = 1,2. (e) Are your eigenvectors orthogonal? That is, does ee2 =0? Did you expect them to be? (f) Normalize your eigenvectors to get the vectors e and e2. Form X, = [e 2]. Find X- (Hint: this should be a simple operation).