Q1. Show all workings.
Don't count the number of divisions. Do not use asymptotic notation, instead provide exact answers.
(i) What is the maximum number of multiplications required to solve a system of n equations with n unknowns using Gaussian Elimination
(ii) What is the maximum number of multiplications required to obtain the determinant of ann by n matrix by L.U. Decomposition using Gaussian Elimination.
(iii) What is the maximum number of multiplications required to invert an n by n matrix using Gaussian Elimination.
(iv) For what range of values of w is the Gaussian-Siedel method stable when solving this system of equations:
3x - y + wz= 3
x + 3y -z = 4
x + y -2z = 1
Q2. Write a procedure to obtain the inverse of an n by n matrix using Gaussian elimination. (You cannot use A-1or any of the built-in packages like 'MatrixInverse'.)
Output any appropriate error statements. Test your procedure on each of these matrices
