# Exercises for Math 1600A Linear Algebra I (Fall 2013)

This course is over. The web page for the current course can be found here.

All exercises are taken from the textbook. The list will be expanded regularly. 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.

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!)

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, 35Only 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, 53, 55 No systems over Zp
Section 2.3  1, 5, 9, 15, 19, 23, 25, 27, 29, 33, 35, 37
Section 2.4  15, 17 Only network analysis
Section 3.1  1, 7, 9, 13, 15, 17, 21, 31, 35, 38(a), 39
Section 3.2  3, 5, 7, 9, 11, 13, 27
Section 3.3  1, 3, 9, 11, 13, 15, 23, 53, 55, 57, 61, 63No elementary matrices or inverses over Zm
Section 3.5  3, 7, 11, 15, 19, 23, 29, 31, 37, 39, 41, 45, 49, 51, 53
Section 3.6  1, 3, 7, 11, 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, 33, 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).

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.