Linear Algebra 1600a Exercises

Exercises for Linear Algebra 1600a, Fall 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! Then do them all again before the exams and quizzes. These should be regarded as the minimum, and it is recommended that you do additional exercises as well. Of course, you should also study the text and your lecture notes, so you understand the concepts behind the problems you are solving.

You should also use the list below to guide your reading of the textbook. You are required to read each section before it is covered in class. We will cover the sections in order.

The odd numbered exercises have answers at the back of the text and solutions in the solutions manual. Solutions to even numbered exercises are on reserve in the library.

Updates to the list below since the beginning of the term are indicated in red.

Section	Exercises
Section 1.1	3, 5, 7, 10, 11, 13, 15, 16, 17, 21, D9
Section 1.2	3, 9, 19, 23, 25, 27, D7, D9; for D7, d(u,v) means the length of u - v
Section 1.3	5, 7, 9, 11, 13, 17, 21, 23, 25, 33, D5
Section 2.1	1, 3, 9, 13, 18, 21, 25
Section 2.2	1, 5, 7, 8, 9, 11, 12, 13, 23, 25, 27, 33, 43, 45, D5, D6, D7, D8; do enough of 10, 14, 24, 26, 28 to be completely comfortable
Section 2.3	not covered
Section 3.1	3, 5, 7, 11, 15, 17(a), 19, 23, D5, D9
Section 3.2	1, 7, 9, 15(a), 17, 21, 24, 25, 32, 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)) (skip p. 139 and top half of p. 140)
Section 3.6	1, 3(a,b), 6, 7, 11, 15, 23, D11 (skip inverting I - A)
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, 23, 29, 33, 35, 37, 45, D3, D4 (skip: adj(A), formula for A^-1, Cramer's Rule, 4.3.6, polynomial interpolation, Vandermonde determinant)
Section 4.4	1, 3, 4, 5, 7, 9, 11, 13, 14, 17, 19, D1, D4, D7(a,b,c), 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, 13, 15(except (d)), D3 (skip Algorithm 2, Example 3, Theorems 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, D1
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

Here are solutions for our midterm.

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.

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