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Math 202 Study Guide for Chapter #5 C.S.Davis |
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Your are responsible for the subject matter in sections 5.1, 5.2 And 5.3 from Elementary Linear Algebra, 5th edition, by Larson and Edwards. The following topics are the most important. Typical exercises are assigned at the end of each topic. If you need more practice than these, work some more similar exercises. |
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5.1 |
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1. |
Use all of the formulas about the dot product, length and angle in calculations. P283#1-79(the first two odd problems of each type) |
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2. |
Use the dot product to prove the triangular inequality. Text |
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5.2 |
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1. |
Give the definition of an inner product space. Text |
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2. |
Give some examples of inner product spaces. Text |
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3. |
Use inner product space as an example to discuss generalization in mathematics. Notes |
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4. |
Evaluate <u,v> for various derinitions of inner product on Rn, Pn, C[-1,1] and Mm,n. P295#5,7,9,11,13,15 |
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5. |
Give examples and non-examples of inner product spaces and show how the definition is either satisfied or fail, respectively. P296#17,21 |
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6. |
Find the angle between vectors in an inner product space. P296#25,29 |
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7. |
Verify the Cauchy-Schwarts inequality and the triangular inequality. P296#31,35 |
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8. |
Determine whether vectors in an inner product space are orthogonal. P297#39 |
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9. |
Find the orthogonal projection of one vector onto another. P297#43,45,49 |
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10. |
Answer true or false questions. P297#51,53 |
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5.3 |
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1. |
Define orthogonal and orthonormal set and basis. Text |
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2. |
Determine whether a basis is orthogonal and/or orthogonormal or neither. P310#1,3,5,7 |
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3. |
Write a vector as a linear combination of an orthonormal basis using Fourier coefficients. P310#13,17 |
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4. |
Perform the Gram-Schmidt orthonormalization process. P310#19,23,29 |