dx x(4 — х — 5у) dt dy = y(1 – 4x), dt taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(4-x)/5 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=4/(x+5) (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (0,0),(4,0),(1/4,3/4) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (5, 3), trajectories converge to v the point (-80,-57) (Enter the point as an (x,y) pair, e.g., (1,2).)

10) Describe a consistent, independent system of linear equations and give examples to justify your response. 1000 character(s) left

Consider the system of linear equations: -x1 + 2x2 + 3x3 + x4 = 3 2x1 - 4x2 + x3 + 2x4 = -1 -3x1 + 8x2 + 4x3 - x4 = 6 x1 + 4x2 + 7x3 - 2x4 = -4 i) Solve the systems of equations for x1, x2, x3, x4 utitilizing the Gauss-Jordan method. ii) Obtain the Lower & Upper triangular matrices for the system of linear equations. iii) Use the LU factorization obtained in iii) to solve for x1, x2, x3, x4. N.b : Don't kindly lift answers from other experts solution.

Use Cramer's Rule to solve (if possible) the system of linear equations. If not possible, enter IMPOSSIBLE 4x1 - X2 + X3 = -7 2x1 + 2x2 + 3x3 = 14 5x12x2 + 6x3 = 8