Problem 1: Consider the equation, 2 sin(x*) = x There is an obvious root x 0, and two non-trivial roots for z (i) Find the first three decimal places for the larger root using several iterations of Newton's method. (ii) Use 10 steps in the bisection method to find the smaller root. Indicate the interval that you choose. Problem 2: Find the eigenvalues and the eigenvectors for the following matrix, 1000 M=10 2 2 2 0 0 2 2 0 0 0 2