Math 544 (Section 001)  University of South Carolina
D. Meade  Fall 1996

Homework Problems for Chapter 4 Vector Spaces and Linear Transformations

Section Page Problems
4.2  306 # 2, 3, 4^{∗}, 6, 7, 8, 10, 11, 17, 18, 19, 25, 27, 28, 29^{∗}, 36
4.3  314 # 1, 2, 4, 6, 7, 8, 11, 14^{∗}, 18, 19, 20, 22, 23^{∗}, 28, 31
4.4  328 # 1, 2, 5, 6, 7^{∗}, 8, 10, 12, 13, 18, 19, 30^{∗}, 31
4.5  333 # 1, 3^{∗}, 4, 5, 6, 7, 8, 9, 10^{∗}, 11, 12, 13
4.6  344 # 1, 3, 4^{∗}, 5, 14, 16, 18, 19^{∗}, 32
4.7  353 # 1, 2, 3, 5, 6^{∗}, 8, 9^{∗}, 11, 12, 13
4.8  362 # 1, 2, 3, 4^{∗}, 5, 7^{∗}, 10
4.9  374 # 1, 2, 3, 4, 5, 6, 8^{∗}, 17^{∗}
4.10  384 # 1, 2, 3, 5^{∗}. 14^{∗}, 15
Review 385 Supplemental Computational Exercises

# 1, 3, 5, 6, 7, 8, 9, 12

Review 387 Supplemental Conceptual Exercises

# 1, 2, 4, 5, 6, 11

\underline{Notes}

• This is the final chapter that we will be discussing. Successful mastery of this material depends critically on the understanding of the topics introduced in Chapter 2: subspace, independence, basis, dimension, ....

• The terminology is critical! If you don’t understand what the question is asking, there is virtually now way to know what the question asks you to do.

• Problems marked with an asterisk (^{∗}) will be collected and graded. In general, problems will be due the day following the lecture in which the section was discussed.

• These problems have been selected as the minimum amount of work that you should be doing for this course. Some problems will be straightforward computations; some will require the construction of a logical argument using the terminology and concepts discussed in class; some problems will require you to expand your knowledge (with given information) and apply this to a new setting.

• If you need more practice, there are many other problems in the text that are similar to the ones I have assigned.

• There are two sections of review problems at the end of each chapter. None of these problems will be collected for grading. These problems should be a good test of your understanding of the main points in the chapter. I suggest solving these problems as one part of your preparation for an exam.

• Be sure you know how to do all of these problems. Do not hesitate to ask questions – in class, by e-mail, or during office hours.