(d) Consider the differential equation system dx/dt = Ax, where x = ($1, x2). Find some appropriate constants q1, 92, 93, 94, such that, if we suppose y1 = q121 + 9212 and y2 = 9341 + 9412, then y1, y2 satisfies the differential equation system dy2/dt = Xy2 and dy / dt = Xy1 + 92.Problem 1. Consider the matrix A = 5 2 -2 (a) Find the eigenvalues of A. Show that A has only one linearly independent eigenvector. (b) Suppose A is the eigenvalue, and v is the eigenvector in (a). Find a vector w such that Aw = Aw+ v. (c) Use (b) to write A into the form A = QPQ-1, where P =