Inverse of an n by n matrix using gaussian elimination

Reference no: EM1382102

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

2110_Gaussian-Siedel method.png

Reference no: EM1382102

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