2. Hilbert matrix H[i,j] = 1./(i+j-1), 1 <=i, j <=N. For N = 100, 200, 500 find the inverse and compute the cond(A) with respect to infinite norm.

3. Consider the following system of nonlinear equations. f(x, y, z) = x**2 + 2y**2 + 4z**2 7 = 0 g(x, y, z) = 2x**2 + y**3 + 6z 10 = 0 h(x, y, z) = xyz + 1 Use Newtons method to find the root. To invert the Jacobian you need to use linpack or lapack routines. For initial guess, use (1.0, -1., 1.2). Iterate until the relative error is less than 10**(-8).