1. Let A = {z € Z]z > 5}, B = {z € Z\z ≤ 2}. (a) Find AUB. (b) Find An B (c) Find A - B (d) Find Be

Program the Gaussian elimination method with no partial pivoting for solving a linear system of the form Ax=b, where b is a single column vector. Your function should take in a coefficient matrix A, and a single input vector b. Your function should return the solution vector x. Your code should also return the appropriate error message. The first line of your function should look like: function x = gaussElimination (A,b)

Use python to solve.

Using Python, to help solve the following problem. Provide an explanation of your solutions to the problem. 4. A symmetric matrix D is positive definite if x¹TDx > 0 for any nonzero vector x. It can be proved that any symmetric, positive definite matrix D can be factored in the form D = LLT for some lower triangular matrix L with nonzero diagonal elements. This is called the Cholesky factorization of D. Consider the matrix [2.25 -3 4.5 -10 -3 5 4.5 -10 34 a. Is A positive definite? Explain. A = b. Find a lower triangular matrix L such that LLT = A.