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Q1) Show all workings.

Do not use asymptotic notation, instead provide exact answers.

(i) What is the maximum number of multiplications need 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 usingGaussian Elimination.

(iv) For what range of values of w is the Gaussian-Siedel method stable when solving this systemof equations:

3x - y + wz= 3
x + 3y -z = 4
x + y -2z = 1

Q2) prepare a procedure to get the inverse of an n by n matrix using Gaussian elimination. (You can't use A-1or any of the built-in packages like `MatrixInverse'.)

Output any appropriate error statements. Test your procedure on each of these matrices

1552_Matrix.jpg

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