Homework Problems for Chapter 4
Vector Spaces and Linear Transformations

• 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.

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