10.5

Determine the total flops as a function of the number of equations n for the  (a) decomposition, (b) forward-substitution, and (c) back-substitution phases of the LU decomposition version of Gauss elimination.

Decomposition
n^3/3 - n/3 or as n increases n^3/3 + O(n)

Forward-substitution
n^3/3 - n/3 + n^2 or as n increases n^3/3 + O(n^2) 

Back-substitution
n^3/3 - n/3 + n^2 or as n increases n^3/3 + O(n^2)