MAT 5410 (Applied Linear Algebra)
Winter 2012, Section 001, CRN 20151
Professor Drucker

ADVICE: Do the exercises as we get to the material on which they’re based. It is essential that you stay ahead in the reading and keep up with the assignments. Don’t allow yourself to fall behind! The items listed in brackets for some sections are MATLAB scripts. If you have access to MATLAB, you should try them before doing the exercises. Some of them illustrate the concepts; others provide computational capabilities that you will find useful when doing the exercises.

Chapter 1. Introduction to Vectors

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1.1 (Review) #1, 4, 6, 9, 11–14, 16, 17, 20, 26

1.2 (Review) # 1, 3, 4, 6–8, 11–13, 16, 21, 27

    In #13, find nonzero vectors v and w.

1.3 (Partially review) #3, 6–8

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Chapter 2. Solving Linear Equations

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2.1 #4, 5, 7, 9, 10, 13, 14, 16–18, 28–30, 33

    The MATLAB scripts and #29, 30 preview Markov matrices.

    See Section 8.3.

2.2 #3, 5–9, 13–15 , 18-23, 25, 26

2.3 #1, 3–5, 7, 11–13, 16–18, 21, 23, 24, 26, 27, 29

    In #12, take advantage of the form of the left-hand matrix in each case.

2.4 #1, 2, 5, 6, 8, 11, 14, 15, 16–18, 20, 21, 26, 28, 32, 33, 35, 36

2.5 [inverse, tridiag] #1, 2, 6, 7, 9, 11, 14, 19, 21, 22, 24–30, 32, 34, 42

2.6 [slu, slv] #5, 7, 10, 12–14, 16–19, 21, 23

2.7 [splu, splv] #1, 2, 4, 6, 7, 11, 16-18, 20, 22, 24, 27, 31, 32, 34, 35

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Chapter 3. Vector Spaces and Subspaces

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3.1 [samespan] #1–6, 8, 10, 11, 14, 15, 18–20, 23, 25, 27, 28, 30, 31

3.2 [findpiv, plu, nulbasis] #1–9, 12, 15, 18, 21, 23, 28, 30, 31, 36

3.3 [elim] #1–3, 7–9, 12, 17-19, 22, 23, 25

3.4 [partic] #1, 3–6, 8, l1–13, 16–20, 22–25, 28, 30, 32–34

3.5 #2, 5, 7, 9, 12, 13–16, 19, 22, 24, 26, 31, 35, 38, 43

3.6 [leftnull, rowbasis, fourbase] #1, 2, 4, 6, 11–14, 18, 21, 24, 25, 28

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Chapter 4. Orthogonality

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4.1 [orthcomp] #3, 6, 7, 10–12, 17–19, 21, 24, 25, 28

4.2 [project, projmat] #1, 3, 5, 7, 8, 11–14, 17, 18, 21, 22, 24, 27

4.3 [linefit, lsq] #1–4, 7, 9, 12, 21, (13–16 optional)

4.4 [grams] #1, 3, 5, 7, 8, 10–14, 18–23, 30, 31, 33, 34

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Chapter 5. Determinants

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5.1 [deter] #1–15, 19, 24, 27–29, 34

5.2 [randperm, signperm] #13, 15, 16, 17, 20, 28

5.3 [cofactor, cramer] #1, 3, 6–8, 10–12, 17–20, 25, 27–29, 31, 32, 34

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Chapter 6. Eigenvalues and Eigenvectors

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6.1 [eigen2, eigshow, eigval, poly2str] #2–10, 12–15, 17–20, 23, 24, 27–29, 32

6.2 [eigvec] #1–4, 7–9, 13, 11–18, 26

6.3 #1, 4, 5, 10, 12, 13, 15, 19, 21–26

6.4 [symmeig, normal] #1, 4–7, 11, 15, 21, 23

6.5 #2–4, 7, 9–12, 15, 20–22, 25, 28

6.6 #1, 3, 5–7, 9, 10, 12, 13, 14 (just READ this one), 15–18, 20

6.7 #1, 2, 4, 6, 9, 11, 12. READ #17.

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Chapter 7. Linear Transformations

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7.1 [house, plot2d] #1–12, 17, 18

7.2 #1, 2, 5–11, 13, 14, 17, 19, 28–30, 32–35

7.4 #1–11, 15–18

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Chapter 8. Applications

Chapter 9. Numerical Linear Algebra

Chapter 10. Complex Vector Spaces and Matrices

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10.1 #7, 8, 14, 16, 21

10.2 #1–12, 14–21, 23–25, 28, 29

10.3 No exercises assigned for this section.

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