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!)
**

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 (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 Z_{p} |

Section 2.3 | 1, 5, 9, 15, 19, 23, 25, 27, 29, 33, 35, 37 | |

Section 2.4 | 15, 17, 19, 21 | Network 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, 57 | No elementary matrices or inverses over Z_{m} |

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 | 5-9 | Only 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 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 | |

Section 5.5 | Not covered. | |

Appendix C | 3, 5, 9, 17, 21, 23, 33, 35 | Numbers 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 **x**_{0}=[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.