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Linear Algebra Fall 2012

Click here for textbook!

HW for Thursday 8/30: Chapter 1, problems 1, 3, 4, 6b, 7

Challenge problem (no due date):  Prove that each of the three Row Operations do not change the set of solutions to a system of linear equations.

HW for Thursday 9/6:
Chapter 1, problems 9, 11, 13, 18, 19e

HW for Thursday 9/13: Chapter 2, problems 1, 3, 4, 5


HW for Thursday 9/20, part 1: Chapter 2, problems 6de, 7a
HW for Thursday 9/20, part 2: Chapter 2, problems 7b, 8, 9a (as written, but also with the matrices in the notes on 9/13/12)

HW for Thursday 9/27, part 1:
Chapter 2, problems 15, 16, 17, 18acf

Challenge Problem (no due date):  Prove that if a square matrix has a left inverse, then it has a right inverse.

HW for Thursday 9/27, part 2: Chapter 3, problems 2pq, 3, 4, 7a, 8

HW for Thursday 10/4: Chapter 3, problems 9, 10

HW for Thursday 10/11, part 1: Chapter 4, problems 1
HW for Thursday 10/11, part 2: Chapter 4, problems 4(for the last part, find all unit vectors perpendicular to both u and v), 5, 6(you should be able to do this without resorting to coordinates), 9(For 9a, compute directly.  For 9b, you must use 9a to deduce it.), 10bdefg

First Maxima Project
Click here to download and install wxMaxima. Please make an appointment with me or go to the ARC if you have never used wxMaxima in a course at Manhattanville before.
I have created two short tutorials about the matrix commands in wxMaxima.  They are Matrix Operations and rowop.
Finally, the instructions for the first project.
This project is due at 11:59PM, Friday October 19 via email to me.

HW for Thursday 10/18, part 1: Chapter 5, problem 1
HW for Thursday 10/18, part 2: First, do the problem assigned in class on Monday, October 8.  Next, Chapter 5, problems 2, 3, 4, 5.

HW for Thursday 10/25:
Chapter 5, problem 6. 
Chapter 6, problem 1 (but also find a basis for the null space in each case).
Chapter 7, problems 1, 2, 3a, 5 (for problems 1 and 2, only find the eigenvalues for now)

HW for Thursday 11/1:
Finish the rest of the Chapter 7 problems, and prove the Cayley-Hamilton Theorem for 2x2 matrices. 

HW for Thursday 11/15:
Chapter 8, problems 1a, 2, 3a, 6.

HW for Thursday 11/29:
Chapter 8, problems 4bcde, 5, 8, 15ac, 16, 19, 21, 22bcd

Second Maxima Project
This project is due at 11:59PM, Monday December 10 via email to me.

HW for Thursday 12/6, part 1:
Chapter 9, problems 1c, 3b, 5b, 10

HW for Thursday 12/6, part 2:
Chapter 9, problems 6, 7, 11, 12, 13

HW due at beginning of final exam:
Chapter 9, problems 15, 16, 17 (for #15, find an orthogonal basis for span{u1,u2, u3} instead.)
Chapter 10, problems 2, 3, 4, 5, 6, 9e
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Paul Ellis,
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Matrix Operations.wxm
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Rowop.wxm
(2k)
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