Homework 4

Turn underlined problems in to the homework boxes in the math department lobby by 3PM on Tuesday 2/12.   Although only the underlined problems should be turned in, you should do the others the day they are assigned to prepare for the quizzes and class discussion the following day.  You may work together and get help from me, tutors, or math friends.  However, the final write-up for the underlined problems must be your own and not copied.  In particular, when you are asked for examples, you should come up with your own, rather than turning in an example from the solutions manual or a friend.  Proofs and explanations should be in your own words.  The assignments will be graded based on your demonstrated understanding of the material, including the quality of your write-up. A numerical answer by itself, with no explanation of your reasoning, will normally receive no credit.  Problems from the text labelled [M] should be done with the aid of the computer or a calculator.  On other problems, you can use your calculator or the computer to check answers, but you should do the computations by hand.   When you use your calculator or the computer on a hand-in problem, you do not need to turn in a printout, but describe essential steps of the computation and give their results on your paper.

Wednesday February 6:

Section 4.6:  3, 6, 10, 16, 17, 19, 23, 27, 35[M]

Also to turn in:  Let Consec(n) be the nxn matrix whose entries are the consecutive integers:  1,2,...n in the first row, n+1,n+2,...2n in the second row, etc.  (We have talked about Consec(2), Consec(3) and Consec(4) in class.)  Experiment in Mathematica to determine the rank of some examples of Consec(n) for different n.  Use your experiments to guess the rank of Consec(n) in general.  Prove your guess. 

Section 4.9:  3, 7, 13, 15[M]

 
Thursday, February 7:
 

Section 5.1:   1, 5, 9, 15, 16, 21, 24, 25, 29, 32

Section 5.2:    1, 7, 9, 12, 17, 18, 19, 27
 

Friday, February 8:

Section 5.3:  1, 3, 5, 7, 15, 21, 24,  3132

Section 5.6:  2, 5, 9, 15, 18[M] (ignore the complex eigenvalues--they have absolute value less than 1, so those terms go to 0)

Monday, February 11:

Section 6.1:   1, 10, 13, 16, 20, 28

Section 6.2:  2, 9, 12, 13,  22, 23, 29

Section 6.3:  4, 7, 11, 14, 21

Tuesday, February 12:

Section 6.5:  1, 3