## Homework:

- Homework questions are assigned from the text 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.)
- The solutions to selected questions are at the end of the textbook.

### 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. 103-109) 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, 9-18 (very good), 19-29 (also very good), 1-8 (extra stuff on vector spaces).

**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 definitely cover 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. 103-109) 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, 9-18 (very good), 19-29 (also very good), 1-8 (extra stuff on vector spaces).

**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 definitely cover 1-8, and 10.