6 problems of numerical methods /Cholesky/ matrix/ some python /. need it in 2 days

Exercise 3

question 1

Given the following matrix:

Check if you can view the A Through the dissolution of Cholesky. If so, find this breakdown, if not, find a breakdown LU. (Check your answer in the Python environment).

Question 2
Given a system of equations , Ax = b When

A. Calculate (without using Python) the decomposition QR for A

B. Use Python and find the system solution by decomposing .QR

Question 3

A. Given the following set of equations:

Use Python and present the first two iterations of the Jacobi method and the Gauss Seidel method, with the first guess for the solution being

B. Given the following set of equations:

Find the system solution using the Gauss Seidel method with accuracy of .

Use the zero vector as an initial guess.

Question 4

Use Python and find the dominant intrinsic value of the following two matrices using the Power Method.

In both cases, perform at least 5 iterations and use a starting vector

Question 5
Given systems of equations	Ax = b The following:

A. Find the solution of each of the systems using the Gaussian extraction method (not in Python).

B. Use Python and find the solution for each of the systems using the following options (if possible).

· Left inverse

· SVD decomposition

· Pinv

Question 6

Given a series of samples of a particular experiment:

Match the series of points in the sense of fewer squares using an exponential curve from the shape