Consider the problem of finding the intersection points of the sphere x2 + y2 + z2 = 4, the circular cylinder x2 + y2 = 1, and the elliptical cylinder 4y2 + z2 = 4.
(a) Use Newton’s method to find one of the intersection points. By choosing a different initial vector x0 = (x0, y0, z0), approximate a second intersection point. (Note: You may wish to use a computer algebra system to determine appropriate inverse matrices.)
(b) Find all the intersection points exactly by means of algebra and compare with your results in part (a).
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