18.06, Fall 2004, Problem Set 1Due before 4PM on Wednesday September 15th, 2004, in the boxes in 2-106. No late homeworkwill be accepted. Don’t forget to write your name and recitation section on the problem set. Thereis one box for each recitation section. For full credit, please be sure to show and explain your work.Exercises refer to the 3rd edition of the textbook.Reading assignment: Sections 1-2.4.1. Exercise 8 from Section 1.2 on page 18.2. Exercise 6 from Section 2.4 on Page 66.3. Exercise 24 from Section 2.4 on page 68.4. Solve the following system of equations by elimination and back substitution:x +2y +3z = 0−x +y −2z = −32x +y +z = 3Let Ax = b denote the above system. Write the three elimination matrices E21, E31and E32that put A into triangular form U with E32E31E21A = U .Compute M = E32E31E21.5. Consider the 3 elimination matrices of the previous exercise. Which of the products E21E31,E21E32and E31E32commute1and which do not? Explain. You actually do not need tocompute the products to answer this question, you can simply reason about what eliminationmatrices do.6. This exercise is to familiarize you with MATLAB on athena. First read the tutorial availableon the course homepage. Now, take your 9-digit MIT ID, say abcdefghi, and construct thefollowing matrix:B =1a + b + c + d + e + f + g + h + ia + b + c e + g + h d + f + id + e + f a + c + i b + g + hg + h + i b + d + f a + c + e.Compute, using MATLAB, B40for your MIT ID (say with just 4 decimals as the usual matlaboutput; you could get more decimals with the format command) and attach the MATLABoutput.As an example, if your MIT ID was 987654321, you could get B in MATLAB with thecommands:>> a=9; b=8; c=7; d=6; e=5; f=4; g=3; h=2; i=1;>> A=[a+b+c e+g+h d+f+i; d+e+f a+c+i b+g+h; g+h+i b+d+f a+c+e]1The product AB commutes (or the matrices A and B commute) if AB = BA.1A =24 10 1115 17 136 18 21>> B=A/(a+b+c+d+e+f+g+h+i)B =0.5333 0.2222 0.24440.3333 0.3778 0.28890.1333 0.4000 0.4667Then you would still need to compute
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