Math 317: Linear Algebra
Final Exam Topics
1. Spanning Sets/Linear Combinations (See in book: 1.1.20, 1.1.21, 1.1.22)
2. Dot Product, Angle Between Two Vectors, Orthogonal Vectors (See in book: 1.2.1,
1.2.2, 1.2.6, 1.2.7, 1.2.11, 1.2.16)
3. Systems of Linear Equations and Gaussian Elimination (See in book: 1.4.2, 1.4.3,
1.4.4, 1.4.5, 1.4.14, 1.4.15)
4. Theory of Linear Systems (See in book: 1.5.1, 1.5.2, 1.5.7, 1.5.8, 1.5.12)
5. Matrix Operations (See in book: 2.1.1, 2.1.5, 2.1.6)
6. Inverse Matrices (See in book: 2.3.1,2.3.2,2.3.8,2.3.9,2.3.11)
7. The Transpose, Symmetric Matrices, Skew Symmetric Matrices (See in book: 2.5.1,
2.5.2, 2.5.5, 2.5.6, 2.5.8, 2.5.11, 2.5.12, 2.5.15)
8. Subspaces of Rn . (See in book: 3.1.1, 3.1.4, 3.1.5, 3.1.6, 3.1.11, 3.1.15)
9. Orthogonal Complements (See in book: 3.1.10, 3.1.12, 3.1.14, 3.1.16)
10. The Four Fundamental Subspaces (See in book: 3.2.2, 3.2.3, 3.2.4, 3.2.6, 3.2.10)
11. Linear Independence and Basis (See in book: 3.3.2, 3.3.3, 3.3.6, 3.3.8, 3.3.9, 3.3.10,
3.3.11, 3.3.14, 3.3.15, 3.3.18, 3.3.19, 3.3.21)
12. Dimension (See in book: 3.4.1, 3.4.3, 3.4.8)
13. Projections (See in book: 4.1.1–4.1.5, 4.1.13, 4.1.15)
14. Least Square Solutions (See in book: 4.1.6–4.1.8)
15. Orthogonal Bases/Gram-Schmidt Procedure (See in book: 4.2.1–4.2.6, 4.2.10)
16. Matrices for Linear Transformations (See in book: 4.3.5, 4.3.7, 4.3.8, 4.3.9, 4.3.11,
4.3.12ab, 4.3.13, 4.3.16)
17. Similar Matrices (See in book: 4.3.17–4.3.21)
18. Determinants (See in book: 5.1.1, 5.1.2, 5.1.4, 5.1.5, 5.1.10, 5.1.11)
19. Eigenvalues/Eigenvectors (See in book: 6.1.1, 6.1.2, 6.1.4, 6.1.8, 6.1.10)
20. Diagonalizable Matrices (See in book: 6.2.1, 6.2.2, 6.2.11)
21. Matrix Powers (See in book: 6.3.1)
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Math 317: Linear Algebra
Final Exam Topics
Additional Details
• Exam 2 will occur in class on Friday, December 18 in our usual classroom from
9:45-11:45 AM.
• In addition to going over the homework, please refer to the examples done in class,
as parts of the exam may resemble these examples.
• Although you have 2 hours to complete the exam, I will be in the classroom at 9:30
AM for those who would like extra time. The exam will conclude at 12 PM.
• No electronic devices may be used on the exam.
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