Consider the vectors x^(1) (t) = (t 1) and x^(2) (t) = (t^2 2t). (a) Compute the Wronskian of x^(1) and x^(2). W(x^(1), x(2)) = (b) In what intervals are x^(1) and x^(2) linearly independent? (Enter your answer using interval notation.) t Elementof (c) What conclusion can be drawn about the coefficients in the system of homogeneous differential equations satisfied by x^(1) and x^(2)? Exactly two of the coefficients of the ODE must be discontinuous at t_0 = 0. One or more of the coefficients of the ODE must be discontinuous at t_0 = 0. All of the coefficients of the ODE must be discontinuous at t_0 = 0. Only one of the coefficients of the ODE must be discontinuous at t_0 = 0. All of the coefficients of the ODE must be continuous at t_0 = 0. (d) Find this system of equations and verify the conclusions of part (c). x' = (0 -1 2/t^2 1/t)x x' = (t -t^2/2 -1 1)x x' = (2/t^2 1 2/t^2 2)x x' = (0 1 2/t^2 -2)x x' = (0 1 -2/t^2 2/t)x