31.1 Draw the phase portrait for the equation dx/dt = Ax when the eigenvalues and eigen- vectors of A are the following: (i) 13 with v₁ = (1, 1) and 2 = -2 with v2 = (1, 2); (ii) complex conjugate eigenvalues λ=-13i, with x < 0 when x = 0 and y > 0; (iii) a single eigenvalue = 13 with eigenvector (3, 2), and x > 0 when x = 0 and y > 0; (iv) 1-2 with v₁ = (2, 1) and 2 = -3 with v2 = (1, -1); = (v) a single eigenvalue = -3 with eigenvector (1, -1), and x > 0 when x = 0 and y > 0; (vi) = ±2i, where y < 0 when y = 0 and x > 0; (vii) = 1 with v₁ = (3, 2) and 2 = 5 with v2 = (1, −4); (viii) =5i, and y >0 when y = 0 and x > 0; and (ix) a single eigenvalue = -7, with the matrix A a multiple of the identity.