MATH 1B03E - SUMMER, 2012

Linear Algebra I

Course Outline

The University is piloting an online version of the course evaluation forms this year.

These evaluations are a very important source of feedback.  Please take the time to complete the course evaluation form at

https://evals.mcmaster.ca

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You will be allowed to use a calculator in the exam.
Only the McMaster standard calculator, the Casio fx 991, is permitted.

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I have uploaded solutions for the sample final on Avenue. Please remember that half the class on Tuesday will cover more material -- material related to dimension, subspaces, rank and nullity.

When you look at the solutions file, please be aware of:

1. Probel 4 part (b) (page 5 of 20) the first sentence of the solution should read : "Since null(A-5I)=2, we have an eigenvalue with geometric multiplicity 2."

It may help you to read the solutions if you know that a square matrix, say n x n, is diagnolizable if and only if the sum of the geometric multiplicities of its eigenvalues in n (it is always less than or equal to n).

The geometric multiplicity will be defined in class. But it is the dimension of the null-space of A-\lambda I (the dimension of the eigenspace).

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Please check avenue for announcements regarding the Final Exam.

In the meanwhile here are some suggested problems from Chapter 4:

You don't have submit these. But do try them and ask for help in class and during office hours.

Section 4.2 : 8a, 12a

Supplementary 4a.

Section 4.3  2, 3, 7b

Section 4.7 3a, 4a, 6a, 6e, 7a, 11b

Section 4.8 2d, 5a, 13.

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Solutions to the sample problems from older tests have been posted on Avenue.

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Dr. Sastry will be in his office by noon for his
office hours today (Wednesday, May 30, 2012).

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Reminder: You have your first midterm tomorrow (May 17) in class. It is for 75 minutes (7pm to 8:15pm). There will be class after the test. The Test has five questions.

I have uploaded a sample test for test 2. This is a sample test from Fall 2011. Some questions will be worked out in class.

Test 2 topics

**In addition to the topics mentioned earlier, Chapter 2 (Determinants) is also on Test
Section 1.7 (some stuff has not been done yet, like the inverse of a symmetric matrix).

Eigenvalues, eigenvectors, diagonalization. In other words 5.1 and 5.2. Ignore Theorem 5.1.6 (since we haven't yet done linear dependence and linear independence).

Complex numbers (see Appendix B pp. 713--719).

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Test 2:
The second mid-term will be on Tuesday, June 5 in class.
The material for the test will be posted later.
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Test 1
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Test 1 will be in class on Thursday May 17. It will cover sections 1.1 to 1.6 of the books. The test will be for 75 minutes and will start at 7 pm. And there will be a lecture after the test (since we are running short of time) .

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ASSIGNMENTS:

Assignment 4:
Your 4th assignment has been posted on WileyPlus. It is due on Tuesday May 29 by 7 PM. _____________
Assignment 3

Your 3rd assignment is up on WileyPlus and due by Thursday May 24.

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Your first assignment has been posted on WileyPlus. The problems are not exactly the one's I announced in class. You need to buy a new book to get the access code. If you are a returning student who took this course last term, you already have an access code. Once you buy the book (with whatever licenses necessary), you need to get onto www.wileyplus.com and look for McMaster University and finally find this course.

GOOD LUCK

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Please look out for your WileyPlus assignment well before the class on Tuesday. The technical issues will be sorted out soon. And do visit this site for updates on the WileyPlus status.

GOOD LUCK