Review sheet for Exam 2

In order to prepare well for the exam you need to review the material below. You also need to review lecture notes, quizzes, and homework. During the exam you will be able to use certain calculators such as TI 83, 84, 85, 86. Please note that programmable calculators, such as TI 89, will not be permitted.

1. Section 3.4. Definition of eigenvalues and corresponding eigenvectors. Review problems: 3, 7, 11, 13, 25, 26 on p. 157.

2. Section 4.1. Review properties of vectors in theorems 4.1, 4.2, and 4.3 (you do not need to memorize statements of these theorems. Review problems: 37, 45, 47, 49, 55, 56, 63 on pp. 189-190.

3. Section 4.2. Definition of a vector space (review this definition, but you do not need to memorize it), examples of vector spaces. Review problems: 13, 15, 17, 19, 21, 27, 37 on pp. 197-198.

4. Section 4.3. Definition of a subspace, Theorem 4.5, Theorem 4.6 (with proof), examples of subspaces. Review problems: 2, 7, 13, 23, 24, 25, 29, 33, 37, 39 on pp. 205-206.

5. Section 4.4. Definitions of linear combination, spanning set, span of a set. Proof that a span(S) is a subspace (see theorem 4.7). Definitions of linear dependence and independence. Theorem 4.8 (with proof), theorem 4.9. Review problems: 3, 11, 17, 19, 29, 31, 33, 37, 39, 41, 45, 53, 54, 57 on pp. 219-220.

6. Section 4.5. Definition of a basis. Theorem 4.9 (with proof), theorem 4.10, theorem 4.11 (with proof). Definition of dimension. Theorem 4.12. Review problems: 17, 21, 27, 37, 41, 43, 47, 51, 61, 71, 76, 77, 78 on pp. 231-232.

Good luck!