Using Python:

Problem 1. rite a program to solve a linear system A b using Gaussian Elimination with scaled partial pivoting and backsubstitution. You can just type in the system matrices at the beginning of the file. Store the matrices as numpy arrays. Recall that scaled partial pivoting works like this. Suppose the matrix we're work on is an n x n matrix W. (Leaving b out of the question. Suppose we're working on column i of W, so we want to zero out the elements below position 22 First, for each row j with i S j S n find the maximum absolute value of the d(i) max jk Then find j in the range j F n that maximizes the quantity d(j) Now switch rows i and j. Proceed to zero out the elements in the rows below the diagonal in column