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- Consider nonnegative integer solutions of the equation x1+x2+x3+x4+x5+x6=30. How many different solutions are there? How many solutions also satisfy: for every i∈{1,2,3,4,5,6}, xi is positive and even?You solve a non-singular system of 1,000 linear equations with 1,000 unknowns. Your code uses the Gauss-Jordan algorithm with partial pivoting using double precision numbers and arithmetics. Why would the 2-norm of the residual of your solution not be zero?The finite difference method transforms the ordinary differential equation in a system of linear equations of the form with k=1,2,...,(n−1) , h=1/n, y0=0 and yn=5 . Knowing this, make n=5 and assemble the associated linear system. Then solve numerically using some iterative method and compare the numerical solution with the exact analytical solution y(x)=x^4+4x . So do the same for n=10 and comment on what you observed. code with python.
- For each of the following pairs of functions ff and gg, circle one of the answers f \in o(g), f \in \Theta(g),fEo(g),fE0(g), or g \in o(f)g€o(f) f(n) = 2", g(n) = (;) Oƒ € o(g9) Oƒ€ 0(g) O gE o(f) %3D %3D i=log2 n f(n) = E" 2', g(n) =n Oƒ € o(g) Oƒ€ 0(g) O gE o(f) %3D %3D f(n) = (210 + 3n)², g(n) = n² Oƒe o(g) Oƒ€ 0(g) Oge o(f) %3D %3D1. Assume that a function f is in polynomial time and can be computed in time 0(n) and that g is in polynomial time and can be computed in time 0(n°). Prove that f composed with g, that is f(g(x)), can be computed in time 0(n5).Solve for the determinants of H and Y. Provide necessary solutions numerically and computationally (using a Python program).Use Google collab or Pycharm
- Let f and g be functions from the positive integers to the positive integers defined by the equations f(x) = 3x + 1, g(x) = x2 + 2, h(x) = 7x - 3 Find the compositions a) g°h (x) b) g° f (x)Make an Algorithm for solving systems of linear algebraic equations using the methods of Cholesky’s decomposition.Find (f o g) and (g o f) , where f (x) =x2+1 and g(x) = x + 2, are functions from R to R.