In class we saw that the computation time can be calculated using Matlab's ticandtoecommands (see the demoTicToc. m). The purpose of this assignment is to investigate the actual computation time for Gaussian elimination for a number of different types of matrices and compare this to theoretical results discussed in lectures. These matrices are as follows: AnNtimesNrandom matrix AnNtimesNrandom, diagonally-dominant matrix AnNtimesNrandom, upper triangular matrix AnNtimesNtridiagonal matrix AnNtimesNtridiagonal matrix stored as a sparse array Code for generating these matrices is given in the fileMatrices. m. Detailed instructions are as follows: bulletChoose an appropriate number of trials and set of values for N. bulletFor each matrix, compute the the average time taken T_avg(N) and plot the data points (log(N), log(T_avg(N))). bulletYou should find that the data follows roughly a straight line. Perform a linear fit of the data and find the slope of the line. bulletFor matrices 1., 2. and 3., discuss how this value relates to theoretical results on 'flop counts'discussed in the lectures. Your conclusions should be explained in a one-page report. In class we saw that the computation time can be calculated using Matlab's ticandtoecommands (see the demoTicToc. m). The purpose of this assignment is to investigate the actual computation time for Gaussian elimination for a number of different types of matrices and compare this to theoretical results discussed in lectures. These matrices are as follows: AnNtimesNrandom matrix AnNtimesNrandom, diagonally-dominant matrix AnNtimesNrandom, upper triangular matrix AnNtimesNtridiagonal matrix AnNtimesNtridiagonal matrix stored as a sparse array Code for generating these matrices is given in the fileMatrices. m. Detailed instructions are as follows: bulletChoose an appropriate number of trials and set of values for N. bulletFor each matrix, compute the the average time taken T_avg(N) and plot the data points (log(N), log(T_avg(N))). bulletYou should find that the data follows roughly a straight line. Perform a linear fit of the data and find the slope of the line. bulletFor matrices 1., 2. and 3., discuss how this value relates to theoretical results on 'flop counts'discussed in the lectures. Your conclusions should be explained in a one-page report