Matlab Gaussian Elimination Algorithm Assignment

1. Like most of the algorithms, Gaussian elimination without pivoting involves a triply nested loop as follows:
   U=A,L=I:
   for k=1 to m-1
   for j=k+1 to m-1
   For j=k+1 to m
   I(K,j)= u(k,j>/u(k,k):
   u( j,kcm)=u( j,km)-(k)u(k,km);
   There are two explicit for loops, and the third loop is implicit in the vectors uj,km) and u(kicm). Rewrite the algorithm with just one explicit for loop indexed by k. Inside this loop, U will be updated at each step by a certain "rank-one outer" product. This "outer product" form of Gaussian elimination if one wants to optimize computer performance. Compare your result with the matlab code for various random matrices with different sizes from 100 to 500.
2. Pivoting has been a standard feature of Gaussian elimination computations since the 1950s. Please write Matlab codes of the Gaussian Elimination with Partial Pivoting and Gaussian Elimination with Complete Pivoting. Compare your result with the matlab code for various random matrices with different sizes from 100 to 500.

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