[LA1600b Home | Exercises]

## Exercises for Linear Algebra 1600b, Winter 2009

Below is a list of the recommended exercises for the course. You are expected to work through all of these exercises as we cover the section in class. This is the best way to learn the material! Don't wait until just before the exams and quizzes to do the exercises.

The odd numbered exercises have answers at the back of the text and solutions in the solutions manual.

 Section Exercises Section 1.1 3, 6, 7, 10, 11, 13, 16, 17, 21, D9 Section 1.2 3, 9, 19, 23, 25, 26, D7; for D7, d(u,v) means the length of u - v Section 1.3 5, 7, 9, 11, 13, 23, 33 Section 2.1 1, 3, 9, 13, 18, 21, 25 Section 2.2 1, 5, 7, 8, 9, 11, 13, 23, 25, 27, 33, 43, 45, D5, D7; do enough of 10, 12, 14, 24, 26, 28 to be completely comfortable Section 2.3 not covered Section 3.1 3, 5, 7, 11, 15, 17(a), 23, D9 Section 3.2 7, 9, 15, 21, 24, 25, 32(a), D5 Section 3.3 1, 3, 5, 7(a), 11, 21, 23, D5 Section 3.4 3, 5, 9, 13, 15, 19, 21, 23, D6 Section 3.5 1, 3, 7, 11, 12, 15, 17(a,b), D1, D4(except (c)) Section 3.6 1, 3(a,b), 6, 7, 11, 15, 23, D11 Section 3.7 not covered Section 3.8 not covered Section 4.1 1, 5, 9, 13, 19, 21, 27, 29, 32 Section 4.2 3, 7(a), 11, 13, 15, 22, 23, 25, 27 Section 4.3 19, 21, 24, 45 (skip 1, 7, 11, 15; adj(A) and Cramer's rule not covered) Section 4.4 1, 3, 5, 7, 9, 11, 13, 14, 19, D1, D4, D8 Chapter 5 not covered Section 6.1 3, 5, 9, 10, 17, 19, 23, 29 Section 6.2 1, 3, 5, 9, 11, 12, 15, 17 (skip pages 288-293) Section 6.3 1, 3, 5, 7, 9, 11, 13, 15, 17, D1 Section 6.4 1, 3, 5, 13, 15, 17, 19, 23(a), 23(b), 27, D1 Section 6.5 not covered Section 7.1 1, 3, 5(b), 7, 8, 9, D3, D4 Section 7.2 1, 3, 5(a), 7, 9, 13, 15, 17, D1 Section 7.3 1, 3, 6, 7, 9, 11, 17, 21, 29, 31, D2 Section 7.4 2, 3, 7, 9, 11, 19, D1, D2; for a challenge: 24; (skip pages 355-357) Section 7.5 1, 3, 5, 7, 9, 13, D4 (except D4(e)); (skip pages 365-366) Section 7.6 1, 3, 7, 9, 11, 13, 15, D3 (skip 7.6.4 and 7.6.5) Section 7.7 1, 3, 5, 7, 9, 11, 13, 15, 17 (skip Strang diagrams, 7.7.7, 7.7.8) Section 7.8 1, 5, 9, 11 Section 7.9 1(b,c), 3(b,c), 5, 7(b), 17, 23, 35, D3 Section 7.10 not covered Section 7.11 1, 3, 7, 9, 13, 17, D2 Section 8.1 1, 3, 5, 7, 9, 13, 15, 17, 21, 27, D4 Section 8.2 1, 3, 5, 7, 9, 13, 15, 19, 21, D2, D3, D4 Section 8.3 not covered

## Self-tests

Here are some self-tests you can do to practice the material.

## Old midterms

You can use these past midterms for practice: November 2005, March 2006, March 2008. They were written by different professors who may have chosen to emphasize different topics, but they will still be good practice. They also cover some material past section 4.4, which won't be on our midterm.

For the 2008 midterm, question 9 should say that det(A) = +4, not -4.

For some questions on these midterms, you need to know that a collection of vectors is called a basis for a subspace if it spans that subspace and is a linearly independent set.

We don't have solutions for these past exams, but here are the answers to the true/false questions:

November 2005, Q16: F T T F T F T T T
March 2006, Q17: T F F T F T T F F T
March 2008, Q11: T T T F F F T

## Old final exams

You can use these past finals for practice: December 2005, April 2005. They were written by different professors who may have chosen to emphasize different topics, but they will still be good practice.

We don't have solutions for these past exams, but here are the answers to the true/false questions:

April 2005, Q11: T T F F skip skip F F T T ((e) and (f) not covered)
December 2005, Q12: T T F T T F T T T F

This page may be updated as the course progresses, so check back often.

Please also check the course web page regularly for announcements and other information.