Consider a non-linear equation system, F(x) = b,
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F, b = 0.
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1. Using Newton’s method, find a root of the system F(x) = b when an initial guess is (x0,y0,z0) = (1,2,3) or (−1,1,1) (with line-by-line code and using the NumPy library).
2. Explain the behavior of Newton’s method when an initial guess is (x0,y0,z0) = (0,0,1).
3. Using broyden2 in the SciPy library, find a root of the system F(x) = b when an initial guess is (x0,y0,z0) = (1,2,3) or (−1,1,1), and compare the result obtained in Question 1.
