Linear Algebra with Applications (3rd Edition)

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ma253 , Fall 2007 — Problem Set Last This is a big assignment. The theory of eigenvalues and eigenvectors is critical and will be the main focus of the final exam. In order find eigenval- ues, you need to understand determinants at least a little bit. This assign- ment tries to get you to really think about both things. Let’s make it due on the last day of classes, Friday, December 7 . 1. Problems from the textbook: a. Section 6 . 1 , problems * 26 , 28 , * 30 , * 32 , * 44 . b. Section 6 . 2 , problems * 4 , * 6 (do these two by hand), * 14 , * 16 , * 18 , * 30 , 50 (the last one is very hard). c. Section 7 . 1 , problems 1 5 , * 6 , * 8 , 15 19 , 33 , * 36 . d. Section 7 . 2 , problems 1 7 , * 8 , * 10 , * 12 , 15 , * 16 , * 28 , * 33 , * 38 . e. Section 7 . 3 , problems 1 5 , * 6 , 7 9 , * 10 , * 14 , * 18 , 35 , 36 , 48 . f. Section 7 . 4 , problems 1 8 , * 10 , * 12 , * 18 . *2. Suppose v is an eigenvector of an invertible n × n matrix A , correspond- ing to an eigenvalue λ . Let I be the identity matrix. a. Is v an eigenvector of A 3 ? If so, what is the eigenvalue? b. Is v an eigenvector of A - 1 ? If so, what is the eigenvalue?
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