LinearAlgebra

Assignments for UE18MA251, Linear Algebra Coded purely from scratch using Python 3.6.x.

Assignment - 1

Given a matrix A for the system of equations Ax = b

• Display, number of equations/rows, number of unknowns/columns, and rank of the matrix. (Use built in functions if required)

• Is the matrix singular (if it is a square matrix)?

• For a given b, will the system Ax = b have

  • Unique solution.
  • Infinitely many solutions
  • No Solution.

• If it has a unique solution display the solution.

Assignment 2

• For a given matrix A which has a unique solution for Ax=b for any b,
  test whether the LU factorization method is faster than the Gaussian Elimination method.

Run a test in this manner: - First read a matrix A with full rank/full column rank. - Generate a hundred random b vectors. - Find a solution for each b. - Note down how long this approach takes.

• Factorize A to LU.
• Generate a hundred random b vectors.
• Find a solution for each b.
• Record how long does this new approach take.

Check if the claim that the first approach takes 100*O(n3/3 ) and the second approach takes O(n3/3 ) + 99*O(n2) is true.