Math 477/577 Computer Assignment 1 Charles Tier
For each question, please submit the Matlab code along with an execution of the code.
1. Define a 6 by 6 integer matrix A= floor(10*rand(6)) and use the sum function to find the
sum of first row and third column of A.
2. Write a script that prompts the user to input two square matrices Aand B. The output should
be the size of the matrices and the sum, difference and product of Aand B. Use comments
in the script and use disp to output titles. It might be useful to look at the script statistics.m
on the Matlab tip page.
3. Write a Matlab script to generate graphs of the functions y= cos xand y= cos(x2)in the
range x=-4:0.02:4 on the same axes. Please label the graphs using xlabel,ylabel, and title.
4. (Leon) Let n= 200 and generate an n×nmatrix and two vectors in Rnboth having integer
entries using
A=floor(10*rand(n));b=sum(A0)0;z=ones(n,1)
(a) Verify that the exact solution of Ax=bis z. Explain why.
(b) The solution of Ax=bcan be found in Matlab using the ”\” operation or by comput-
ing A−1and finding A−1b.Compare the speed of the two methods using Matlab’s tic
and toc commands to measure the elapsed time for each computation. Which method
is faster?
(c) Compare the accuracy of the two methods using the command: max(abs(x-z)). Explain
what is being measured and which method is more accurate.
(d) repeat if n= 1000.
5. Write a function col-sum that generates a random square matrix Aof specified size nand
then finds the sum of each column using:
(a) for loops
(b) the sum function
Test the function with n= 10,50.