Exercises for Math 1600A Linear Algebra I (Fall 2014)

All exercises are taken from the textbook. The list may be adjusted as the term progresses. New questions will be in red, and deleted questions will be stroked out.

If we don't cover a section completely, the comments column below will indicate this, but this may also change as the term progresses.

If a question number is a hyperlink, then clicking on the link will provide more information about the question.

In order to become familiar with the material, you will probably have to solve more exercises than the ones given below. (Recall that the questions in quizzes and exams will not simply be these exercises with changed numbers!)

SectionExercisesComments
Section 1.1  1, 3, 5, 7, 9, 11, 13, 17, 21, 29, 33, 43, 55The dot product is defined in Section 1.2.
Section 1.2  3, 9, 15, 17, 25, 33, 41, 47, 49, 66
Section 1.3  1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 27, 29
Cross products  1, 2, 4, 8(c)Know the properties listed in Ex. 5 (but not Ex. 6)
Section 1.4  15, 17, 19, 21, 23, 27, 31, 35 (click for solution)Only code vectors
Section 2.1  1, 3, 9, 11, 13, 15, 17, 21, 23, 29, 31, 37
Section 2.2  5, 7, 9, 11, 15, 21, 23, 29, 31, 33, 35, 37, 45, 47, 49 No systems over Zp
Section 2.3  1, 5, 9, 15, 19, 23, 25, 27, 29, 33, 35, 37
Section 2.4  15, 17, 19, 21Network analysis and electrical networks
Section 3.1  1, 7, 9, 13, 15, 17, 21, 31, 35, 38(a), 39
Section 3.2  3, 5, 7, 13, 27
Section 3.3  1, 3, 9, 11, 13, 15, 23, 53, 55, 57No elementary matrices or inverses over Zm
Section 3.5  3, 7, 11, 15, 19, 23, 29, 31, 37, 39, 41, 45, 51
Section 3.6  1, 3, 7, 11, 13, 17, 20, 21, 31, 37, 40 (look at 38(a) in Sec. 3.1 if you're stuck)
Section 3.7  5-9Only Markov chains
Section 4.1  5, 7, 11, 13, 21, 23, 27, 29, 37
Section 4.2  5, 9, 13, 23, 27, 29, 31, 33, 39, 45, 49, 51, 53, 57, 59, 61
Section 4.3  1, 3, 5, 7, 9, 11, 15, 19, 23
Section 4.4  1, 3, 7, 9-15, 19, 21, 25, 37
Section 4.6  7 and also see belowOnly Markov chains?
Section 5.1  3, 5, 7, 9, 13, 15, 17, 19, 21, 29, 31Only check for rotations in Ex. 29 and 31
Section 5.2  1, 3, 5, 7, 9, 11, 13, 17, 21
Section 5.3  1, 3, 5, 7, 9, 11, 13, 15
Section 5.4  3, 5, 9, 13, 17, 21
Section 5.5  Not covered.
Appendix C  3, 5, 9, 17, 21, 23, 33, 35Numbers refer to the "Appendix Exercises" (copy here; solutions).

Exercise for Section 4.6: Take the matrix from Exercise 7 in that section.
a) Find the equilibrium state y for a total initial population of 10.
b) Show that in the long run any initial state x0=[a,b] with a+b=10 tends to the equilibrium state y found in (a).
Solution.

Here are five practice midterms: MT Winter 2014, MT1 Winter 2013, MT2 Winter 2013, MT1 Fall 2013, MT2 Fall 2013.

Here are the same five exams, with solutions: MT Winter 2014, MT1 Winter 2013, MT2 Winter 2013, MT1 Fall 2013, MT2 Fall 2013. Try the problems first without looking at the solutions!

Both of the MT1 exams cover less than our midterm will cover, and both of the MT2 exams go further. So when studying from the MT2 exams, if there is a topic we haven't covered, you don't need to worry about it.

Here are the solutions to our midterm.

Final exam practice New!

No practice final exams are available, but here are some resources:

All of the homework problems above.

The practice midterms above, especially the two "MT2" exams, since they were late in the semester.

Section 3.5: exercises 1, 5, 17, 21, 25, 27, 35, 47.

Section 3.6: exercises 9, 15, 38.

Section 4.1: exercises 1, 3, 9, 17, 28.

Section 4.2: exercises 1, 7, 11, 25, 37, 38.

Section 4.3: exercises 21, 25.

Section 4.4: exercises 5, 40, 41.

Section 5.1: exercises 1, 11.

Section 5.2: exercises 19, 25.

Section 5.3: exercises 4, 6, 8, 10, 16.

Section 5.4: exercises 1, 7.