**Assignment 1** - Due Friday, June 3, 2016

- Read sections 1.1-1.5 and my Notes on Row Reduction.
- Do the following problems.
- Section 1.1 (pgs. 10, 11): 6(c,d,f), 7
- Section 1.2 (pgs. 23-26): 3(d,f) 5(e,j,k), 8,9, 22(b)
- Section 1.3 (pgs. 42-44 ): 1(b,d,e), 2(b,f), 10(a,c). (To do
10(a,c), first use the basic matrix trick (boxed eqn. on p. 34) to
find A
**x**for all**x**. Then, use Theorem 3.1.)

- Point distribution: 1.1.6(d) -- 20 pts. 1.7 -- 20 pts. 1.2.3(f) -- 5 pts. 1.2.9 -- 20 pts. 1.2.22(b) -- 20 pts. 1.3.2(f) -- 5 pts. 1.3.10(c) 10 pts.

**Assignment 2** - Due Wednesday, June 8, 2016

- Read sections 2.1, 2.2, 3.1, 3.2
- Do the following problems.
- Section 1.4 (pg. 56): 7, 9, 12 (You may assume
a
_{11}≠ 0.), 13(b), 15, 21 - Section 1.5 (pgs. 66-67): 5(a,b,c), 7(a,b), 10(d,f,h)
- Section 2.1 (pgs. 94-95): 3(d,g), 5 (Use the cofactor method for these.)
- Section 2.2 (p. 101): 2(a,b), 3(e,f), 4, 5, 6

- Section 1.4 (pg. 56): 7, 9, 12 (You may assume
a
- Point distribution: 1.4.12 -- 10 pts. 1.4.21 -- 10 pts. 1.5.5(b) -- 5 pts. 1.5.7(b) -- 10 pts. 1.5.10(f) -- 15 pts. 2.1.3(g) -- 20 pts. 2.2.2(a) --15 pts. 2.2.4 --10 pts. 2.2.6 --5 pts.

**Assignment 3** - Due Friday, June 10, 2016

- Read sections 3.3, 3.4
- Do the following problems.
- Section 3.2 (pgs. 131-132): 1(a,d), 2(a,b), 3(b,d,f), 4(a,d), 5(a,d), 6(a,b,e), 7

- Point distribution: 3.2.1(a,d) -- 20 pts. 3.2.2(b) -- 10 pts. 3.2.3(d) -- 5 pts. 3.2.4(d) -- 15 pts. 3.2.5(a,d) -- 20 pts. 3.2.6(b,e) -- 20 pts. 3.2.7 --bonus, 5 pts.

**Assignment 4** - Due Tuesay, June 14, 2016

- Read section 3.6, 4.1, and the notes on Methods for Finding Bases.
- Do the following problems.
- Section 3.2 (pgs. 131-132): 12(d,e), 16(a,b)
- Section 3.3 (pgs. 143-144): 2(c,e), 4(c), 10
- Section 3.4 (pgs. 149-150): 2(c,e), 13, 14(b,d)
- Section 3.6 (pgs. 165-166): 1(a,b), 3(a,b), 9, 14
(Note:
a _{1},a _{2},a _{3}a _{4}are the columns of the original matrix.)

- Point distribution: 3.2.12(e) -- 10 pts. 3.2.16(b) -- 15 pts. 3.3.2(c) -- 15 pts. 3.3.4(c) -- 10 pts. 3.4.13 -- 10 pts. 3.4.14(b) -- 15 pts. 3.6.1(b) -- 15 pts. 3.6.14 -- 10 pts.

**Assignment 5** - Due Tuesay, June 21, 2016

- Read sections 3.5, 4.1-4.3, and the notes on Coordinate Vectors and Change of Basis.
- Do the following problems.
- Section 3.5 (pg. 159): 3, 4, 6
- Find the transition matrix S
_{E → F}if E = {1, x, x^{2}} and F = {1-x, 2x+x^{2}, x^{2}-1} - In
**R**^{2}, find the transition matrix S_{E → F}if E = {(1 -1)^{T}, (1 1)^{T}} and F = {(2 -1)^{T}, (1 2)^{T}}. - Section 4.1 (pgs. 182-183): 4, 6(a,b,d), 10, 17(c), 19
- Section 4.2 (pgs. 195-196): 5(a), 15
- Let L : P
_{3}→ P_{3}be defined by L[p]= (2x^{2}+ x + 1)p'' − (3x − 1)p' + 2p.- Show that L is linear.
- Find the matrix A of L relative to the standard basis E = {1, x,
x
^{2}}. - Find bases for the null space, and column space of A.
- Use the bases you found above to write down bases for the null space and image of L, in terms of polynomials.
- Use the matrix A to solve for the polynomial p if L[p] = 3 − x.

- Point distribution:
**(1)**3.5.4 -- 10 pts.**(2)**-- 10 pts.**(4)**4.1.6(b) -- 5 pts. 4.1.6(d) -- 5 pts. 4.1.19(c) -- 10 pts.**(5)**4.2.5(a) -- 10 pts.**(6)**50 pts. (10 pts. per part.)

**Assignment 6** - Due Friday, June 24, 2016

- Read sections 5.1, 5.2, 5.3
- Do the following problems.
- Section 4.3 (pgs. 202-203): 4, 5(a,b,c), 6(a,b,c), 11
- Section 5.1 (pg. 225): 17, 18
- Section 5.2 (pg. 233): 1(b,c), 4

- Point distribution: 4.3.4 -- 20 pts. 4.3.6(a) -- 10 pts. 4.3.6 (b) -- 10 pts. 4.3.6(c) -- 5 pts. 5.1.18(a) -- 10 pts. 5.1.18(b) -- 5 pts. 5.2.18(c) -- 20 pts. 5.2.4 -- 20 pts.

**Assignment 7** - Due Tuesday, June 28, 2016

- Read sections 5.5 (pgs. 253-260), 6.1, 6.2 (2nd application), 6.3
- Do the following problems.
- Section 5.3 (pg. 243): 5(a), 7
- Section 5.5 (pg. 269-270): 1(b,c), 4, 15, 21(a,b(iii))
- Section 6.1 (pg. 308): 1(c,d,g,h), 3, 4, 13

- Point distribution: 5.3.5(a) -- 20 pts. 5.3.7 -- 15 pts. 5.5.15 -- 5 pts. 5.5.21(b(iii)) -- 20 pts. 6.1.1(h) -- 20 pts. 6.1.4 -- 5 pts. 6.1.13 -- 15 pts.

**Assignment 8** - Due Thursday, June 30, 2016

- Read sections 10.2, 11.2, 11.3
- Do the following problems.
- Section 10.2 (pg. 685): 10, 17
- Section 11.2 (pg. 739): 9(a), 14
- Section 11.3 (pg. 755): 4, 5

- These problems are for practice. We will discuss them in
class. Don't turn them in.
- Section 11.3 (pg. 755-757): 18, 20
- Verify Stokes's Theorem in case
**F**= 2y**i**+ 3x**j**− z^{3}**k**and S is the upper hemisphere of x^{2}+ y^{2}+ z^{2}= 4, which has the circle x^{2}+ y^{2}= 4, z = 0, as a boundary. Use the normal with positive z component.

- Point distribution: 10.2.10 -- 20 pts. 11.2.9(a) -- 20 pts. 11.3.4 -- 40 pts. 11.3.5 -- 20 pts.

Updated 7/1/2016 (fjn)