• The nonlinear system 4x1 − x2 + x3 = x1x4, −x1 + 3x2 − 2x3 = x2x4, x1 − 2x2 + 3x3 = x3x4, x2 1 + x2 2 + x2 3 = 1 has six solutions. (a) Show that if (x1, x2, x3, x4)T is a solution then (−x1, −x2, −x3, x4)T is a solution. (b) Show how to solve the nonlinear system via the computation of all the eigenvalues and eigenvectors of a 3 × 3 matrix.