Algorithm 7 : Enumerating All Base Images Input : a permutation group G; a base and strong generating set for G; the Schreier vectors v (i) , 1 < i < k, of the stabiliser chain; Output : the base images of the elements of the group G (without repetition);

In pythion with numpy I have code in a for loop that creates a vecor of 12 elements:x = 1 2 3 4 5 6 7 8 9 10 11 12 The loop iterates 10 times.  The second iteration generates a new vector x = 12 11 10 9 8 7 6 5 4 3 2 1 etc. At the end of the loop I need to have a 12 X 10 matrix x x x x x x x x x x  x x x x x x x x x xx x x x x x x x x x  x x x x x x x x x xx x x x x x x x x x  x x x x x x x x x xx x x x x x x x x x  x x x x x x x x x xx x x x x x x x x x  x x x x x x x x x xx x x x x x x x x x  x x x x x x x x x x I cannot figure out how to createa matrix where it takes the output and uses the output as row

Algorithm for Testing MembershipInput : a group G acting on f~ = { 1,2 ..... n };a permutation g of f~ = { 1,2 ..... n };a base and strong ~enerating set for G;Schreier vectors v (i) , 1 < i < k, for the stabiliser chain;Output: a boolean value answer, indicating whether g ~ G;function is_in_group(p : permutation; i : 1..k+l ) : boolean;(* return true if the permutation p is in the group G (i) *)

1. Implement a helper function called rref pp (A, b) that applies Gaussian Elimination with partial pivoting to return the Reduced-Row Echelon Form of the augmented matrix formed from Matrix object A and Vec object b. The output must be of the type Matrix. 2. Implement the function solve pp(A, b) that uses rref pp (A, b) to solve the system A = b. The input A is of the type Matrix and b is of the type vec. o If the system has a unique solution, it returns the solution as a Vec object. o If the system has no solution, it returns None. o If the system has infinitely many solutions, it returns the number of free variables (int) in the solution. def _rref_pp(A, b): # todo pass def solve_pp(A, b): #todo pass Python