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.

If a question number is a hyperlink, then clicking on the link will provide more information about the question. (Currently only question 31 in Section 2.2.)

**
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 | Exercises | Comments |
---|---|---|

Section 1.1 | 1, 3, 5, 7, 9, 11, 13, 17, 21, 29, 33, 43, 55 | The 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 | 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 Z_{p} |

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, | |

Section 3.3 | 1, 3, 9, 11, 13, 15, 23, 53, 55, 57, | No elementary matrices or inverses over Z_{m} |

Section 3.5 | 3, 7, 11, 15, 19, 23, 29, 31, 37, 39, 41, 45, | |

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 | 5-9 | Only Markov chains |

Section 4.1 | 5, 7, 11, 13, 21, 23, 27, 29, | |

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 below | Only Markov chains |

Section 5.1 | 3, 5, 7, 9, 13, 15, 17, 19, 21, 29, 31 | only 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 | |

Not covered. | ||

Appendix C | 3, 5, 9, 17, 21, 23, 33, 35 | Numbers 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 **x**_{0}=[a,b] with a+b=10
tends to the equilibrium state **y** found in (a).

Solution.