## Homework:

- Homework questions are assigned from the text (4th and 3rd editions) and you will benefit greatly from working your way through them.
- (Of course, you are welcome to work on more than these subsets if you like.)
- Solutions to some selected questions are at the end of the textbook.

### Edition 4 of the Textbook (Edition 3 is below):

**Section 1.1:**(pp. 6-10) A, B, 1, 2, 4, 6, 9, 10, 13, 20, 22, 25, and, for a challenge, 28.

**Section 1.2:**(pp. 17-21) A, B, 1, 2, 3, 5, 7, 8, 13, 19, 27, and 29.

**Section 1.3:**(pp. 27-30) A, B, 1 (odd wording but good), 3, 5 and 6 (more later), 14 (challenge, good).

**Section 2.1:**(pp. 39-44) A, B, 1-4, 6-8, 9, 10, 11, 12, 13a, 14, 15, 19, 26, 29 (challenge, Sudoku!), if you like computers, 23, 24, 25.

**Section 2.2:**(pp. 50-55) A, B, 1-9, 11, 12, 13, 14, 16a (trickier) 25, 26 (sneaky), 32 (challenge).

**Section 2.3:**(pp. 61-66) A, B, C (nutritious), 1, 2, 3, 4, 5, 6 (good for understanding), 9a, 10 (wax on, wax off), 16 (terrific), 19, 20, 23, 24, 25, 28.

**Section 2.4:**(pp. 72-80) B and C (networks!), (A is very good but view as extra material), 1, 2, 3, 5, 6, 7, 8, 9 (all preceding = good training), 11, 14, 17a, 17b, 18a, 21, 24a, 26, 27 (important), 28.

**Section 2.5:**(pp. 77-83 ) A, B (optional---more for those with a math focus), 1, 2, 4, 5, 6, 7, 8, 11, 12, 15, 18 (clear thinking), 22 (find the inverse), 28, 29 (good puzzling), 31, 32 (why not), 40 (good challenge), 46 (be a hero).

**Section 2.6:**(pp. 101-106) 1 (please do), 2, 3, 5, 6, 12, 13 (excellent value), 15, 22, 23.

**Section 2.7:**

All about transposes and symmetric matrices:

(pp. 114-119) 1-7 (working with transposes), 16-21 (symmetric matrics and factorization, all good).

**Section 3.1:**(pp. 126-131) A, B, 9-18 (very good), 19-29 (also very good).

**Section 3.2:**(pp. 139-143) A, B, (1-4, terrific), (5-8, nom, nom, nom), 9, 10, 11, 18, 20; puzzles follow: (21-24, a festival), 26, 27, 30, 31, 32, 33a.

**Section 3.3:**(pp. 149-154) A (it's all happening), B (foreshadowing of magic), 1, 2, 3, 4, 8-11 (more foreshadoning, cue dramatic music), 12 (yes!), 13, 15 (very interesting to think about).

**Section 3.4:**(pp. 160-167) (A, B, C, absorb all these grasshoppers), (1-8, full solution stuff, all good), 11, 13 (thinkage), 16, 17, 18, 22, (23-25), (26, 28, 29, 30, 33, Gauss-Jordan goodness).

**Section 3.5:**

(pp. 177-183) A, B (really good), C (tougher, important), 1, 2, 3, 5, 11, 12, 16, 25 (great!), 26 (interesting), 27, 28.

**Section 3.6:**

(pp. 190-194) A (solid four subspaces example), B (good puzzle); do these!: 1, 2, 4, 5, 6, 7, 8, 16, 17, 24.

**Section 4.1:**

(pp. 201-205) A, B, 3 (good puzzles), 4, 5, 11 (very healthy), 12, 13, 16, 17, 19, 21, 28, 29.

**Section 4.2:**

(pp. 213-217) A, 1, 3, (5, 6, 7—a good set), 11, 13, 17 (important!), 19, (21, 22, 23 ,24—good thinking here), 27, 30 (curious and conceptual).

**Section 4.3—Approximate Solutions:**

(pp. 225-229) A, B, (1, 2, 3, 5, 7, 9—all good), 12 (important), 17, 18.

**Section 4.4—Orthogonality and the Gram-Schmidt Process:**

(pp. 238-243) A (good example of why orthogonality matters), 1, 2, 3, 4, 6, 7 (good), 10b, 11 (good), 13, 15, 16, 18, 20, (33, 34: reflection matrices, slightly harder).

**Section 6.1—Eigenstuff:**

(pp. 291-297) A (read straight away), B (examine later), 2, 7, 8, 11 (tricksy), 13, 16, 17, 18 (good), 19, 20, 22, 28, 30 (a winner).

**Section 5.1—Determinants:**

(pp. 250-254) A, B, 2 (yup), 3, 4, 7, 8a, 8b (harder and good), 9, (10, 11, 12, all good thinking questions), 13, 14, 15, (optional: any of 17-23), 24 (must do), 28 (true/false), 29 (good).

**Section 5.2—Cofactors:**

(pp. 262-268) A, 11, 12, 15 (good), 17, 18 (Fibonacci!), 21, 22, 33 (a challenge).

**Section 5.3—Cramer's Rule and inversiveness:**

(pp. 277-282) A, B (for increased understanding, not so practical numerically), 1, 2a, 3, 5 (good for thinking), 6a and/or 6b, 7 (thinking), 8, 9, 10 (quick proof question), 11 (professorial challenge).

**Section 6.2—Diagonalization (joy):**

(pp. 306-311) A, B, 1 (ground level, must do), 2, 3, 4, 5 (must be in brain), 6, 7 (good), 8 (Fibonaccilicious), 9 (Gibonacci!), 14 (#fail), 15, 19, 20 (please do!), 22 (delicious), 29 (good thinking), 31 (Cayley Hamilton), 33 (networks!).

**Section 6.4—Diagonalization and Symmetric Matrices (symphonic):**

(pp. 336-341) 1, (a few of 3, 4, 5, and 6), 7, 8 (good), 10, 11 (important), 18 (good), 21 (good), 25 (good).

**Section 6.5—Positive Definite (very assured) Matrices:**

(pp. 348-354) 1 (do this), 2, 3 (important), 5, 6 (solidity), 7 (do one or more), 9 (excellent), 10, 12, 19, 22 (enjoyably good), 25 (Cholesky factorization), 30.

**Section 6.6—Similar matrices and basis transformation:**

(pp. 359-362) 1, 5.

**Section 6.7—The Truth of Singular Value Decomposition (SVD):**

(pp. 370-373) A (a big deal), (1, 2, 3) (please do), (4, 5, 6, 7) (worthwhile), 9 (good, general), 10 (specific), 11 (tougher), 12 (key), 15 (thinking).

**Bonus:**

- Review p. 374 formulae.
- Read over p. 574's `linear algebra in a nutshell.'
- Delight in the Conceptual Questions for Review on pp. 552-556.
- Delve into the glossary on pp. 557-563.
- Examine the major matrix formulations on pp. 564 and 565. The course covers 1-8 and 10.

### Edition 3 of the Textbook:

**Section 1.1:**(pp. 6-10) A, B, 1, 2, 4, 6, 9, 10, 13, and, for a challenge, 28.

**Section 1.2:**(pp. 17-20) A, B, 1, 2, 3, 5, 7, 8, 13, and 29.

**Section 2.1:**(pp. 29-34) A, B, 1-4, 6-8, 10a, 11a, 14a, 14b, 15, 16, 17, 27, 28, 29, and, if you like computers, 30, 31, 32.

**Section 2.2:**(pp. 40-45) A, B, 1-9, 11, 12, 13, 15a, (trickier) 16, 18, 19 25

**Section 2.3:**(pp. 51-56) A, B, C, 1, 2, 3, 4, 5, 6, 9a), 10, 16, 19, 20, 23, 24, 25, 28.

**Section 2.4:**(pp. 62-70) B, (A, C very good but view as extra material) 1, 2, 3, 5, 6, 7, 8, 9 11, 14, 17a, 17b, 18a, 21, 24a, 26, 27 (important), 28.

**Section 2.5:**(pp. 77-83 ) A, B (optional---more for those with a math focus), 1, 2, 4, 5, 6, 7, 8, 11, 12, 15, 18, 22, 28, 29, 30.

**Section 2.6:**(pp. 91-96) 1, 2, 5, 6, 12, 15, 22, (25, 26, both harder). If you get along well with computers: 32, 33, 35; A and B are a good challenge.

**Section 2.7:**

All about transposes and symmetric matrices:

(pp. 114-119) 1-7, 16-21, plus please examine the `transparent proof' on page 109 of why (AB)

^{T}= B

^{T}A

^{T}.

**Section 3.1:**(pp. 116-121) A, B, 9-12, 14, 17, 18, 19-29 (also very good).

**Section 3.2:**(pp. 129-133) A, B, (1-4), (5-8), 9, 10, 11, 18, 20, (21-24, a festival), 26, 27, 30, 31, 32, 33a.

**Section 3.3:**(pp. 139-144) A, B, 1, 2, 3, 4, 6, 12, 13, 15.

**Section 3.4:**(pp. 149-156) A, B, C, (1-8, full solution stuff, all good), 11, 13, 16, 17, 18, 22, (23-25), 26, 28, 29, 30, 33.

**Section 3.5:**

A, 1, 2, 3, 5, 11, 12, 16, 25, 26, 27, 28; also: B and C (tougher).

**Section 3.6:**

B, 1, 2, 4, 5, 6, 7, 8, 16, 17, 24.

**Section 4.1:**

A, B, 3, 4, 5, 11, 12, 13, 16, 17, 19, 21, 28, 29.

**Section 4.2:**

A, 1, 3, (5, 6, 7—a good set), 11, 13, 17 (important!), 19, (21, 22, 23 ,24—good thinking here), 27, 30 (curious and conceptual).

**Section 4.3—Approximate Solutions:**

A, B, (1, 2, 3, 5, 7, 9—all good), 12 (important), 17, 18.

**Section 4.4—Orthogonality and the Gram-Schmidt Process:**

(pp. 227-232) A (good example of why orthogonality matters), 1, 2, 3, 4, 6, 7 (good), 10b, 11 (good), 13, 15, 16, 18, 20, (33, 34: reflection matrices, slightly harder).

**Section 6.1—Eigenstuff:**

(pp. 282-288) A (read straight away), B (examine later), 2, 7, 8, 11 (tricksy), 13, 16, 17, 18 (good), 19, 20, 22, 28, 30.

**Section 5.1—Determinants:**

(pp. 239-244) A, B, 2, 3, 4, 7, 8a, 8b (harder and good), 9, (10, 11, 12, all good thinking questions), 13, 14, 15, (optional: any of 17-23), 24, 28 (true/false), 29 (good).

**Section 5.2—Cofactors:**

(pp. 252-259) A, 11, 12, 15a, 15b (good), 17, 18 (Fibonacci!), 21, 22, 36 (a challenge).

**Section 5.3—Cramer's Rule and inversiveness:**

(pp. 268-273) A, B (for increased understanding, not so practical numerically), 1, 2a, 3, 5 (good for thinking), 6a and/or 6b, 7 (thinking), 8, 9, 10 (quick proof question), 11 (professorial challenge).

**Section 6.2—Diagonalization (joy):**

(pp. 296-303) A, B, 1 (ground level), 2, 3, 4, 5 (must be in brain), 7, 8 (good), 9 (Fibonaccilicious), 10 (Gibonacci!), 14, 17 (interesting), 19, 20 (please do!), 22 (delicious), 24, 25 (fun with the trace), 29 (good thinking), 36 (Cayley Hamilton), 38 (see 29).

**Section 7.3—Changing bases:**

(pp. 388-390) 1, 6.

**Section 6.4—Diagonalization and Symmetric Matrices (symphonic):**

(pp. 325-330) 1, (a few of 3, 4, 5, and 6), 7, 8 (good), 10, 11 (important), 18 (expanding), 19, 20 (eigenvalues versus pivots), 21 (good), 23 (hmmm), 25 (good), 26 (challenge).

**Section 6.5—Positive Definite (very assured) Matrices:**

(pp. 338-342) 1 (do this), 2, 3 (important), 5, 6 (solidity), 7 (one or more), 9, 10, 12, 19, 22 (enjoyably good), 25 (Cholesky factorization), 30.

**Section 6.7—The Truth of Singular Value Decomposition (SVD):**

(pp. 359-361) A (a big deal), (1, 2, 3) (please do), (4, 5, 6, 7) (worthwhile), 8 (good, general), 9 (specific), 10 (tougher), 11 (key), 15, 16 (thinking).

**Bonus:**

- Review p. 362 formulae.
- Read over p. 568's `linear algebra in a nutshell.'
- Delight in the Conceptual Questions for Review on pp. 546-550.
- Examine the major matrix formulations on pp. 544 and 545. The course will covers 1-8 and 10.