Determine multiplications required to obtain the determinant, Mathematics

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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 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

 


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