5. Complete MGHW6 before beginning this problem. The following system of equations has two different solutions: xy - z 2 = 10 yzxy = 1 xyz = 4 (a) (2 points) Let x = [x; y; z] so that we can write x1 Write down the vector-valued function in terms of problem f(x) = 0. for x, x2 for y and x for z. that defines the root-finding (b) (3 points) Write down the 3x3 Jacobian matrix for the system in terms of I. (c) (3 points) If I start with the initial guess corresponding to x = y = z = 1, I get a warning statement, and an answer that doesn't make any sense. Reproduce this in Matlab (nothing to turn in for that, but this will help you answer the question). Evaluate the Jacobian at your initial guess by hand. Turn in three things: (1) write out this matrix, (2) use this result to explain the warning statement and why Newton's method for systems failed to give a reasonable answer, and (3) explain how you could fix this problem. (d) (3 points) Find both roots of the system. Express your answer as a point in R using the notation (x, y, z). Report at least 4 digits after the decimal place (consistent with format about in Matlab).