4. Draw the zeroclines (the functions of the vector space set equal to zero) for the following system of equations. dx dt dy dt = 2x2x² - xy,, = 2y - xy - 2y². (3) Use the zeroclines for a) to find the equilibrium points of the system. b) Label the equilibrium points in the drawing of the zeroclines and their coordinates. c) Calculate the Jacobian and classify each equilibrium point (source, spiral, sink, etc.).

Could you answer part b) for me please?

Show that the vectors p1(x) = a + bx and p2(x) = c + dx are linearly independent in P1(R) if and only if the constants a, b, c, d satisfy ad − bc ≠ 0

Find a vector parametric equation r(t) for the line through the points P = (4, −3, 4) and Q = (3, −6, 2) for each of the given conditions on the parameter t. (a) If 7(0) = (4, −3, 4) and 7(2) = (3, −6, 2), then r(t) = (b) If 7(6) = P and 7(8) = Q, then r(t) = = (c) If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then F(t) =