Math 311-100 Assignments — Summer I, 2016

Assignment 1 - Due Friday, June 3, 2016

• Read sections 1.1-1.5 and my Notes on Row Reduction.
• Do the following problems.
  1. Section 1.1 (pgs. 10, 11): 6(c,d,f), 7
  2. Section 1.2 (pgs. 23-26): 3(d,f) 5(e,j,k), 8,9, 22(b)
  3. 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 Ax 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.
  1. Section 1.4 (pg. 56): 7, 9, 12 (You may assume a₁₁ ≠ 0.), 13(b), 15, 21
  2. Section 1.5 (pgs. 66-67): 5(a,b,c), 7(a,b), 10(d,f,h)
  3. Section 2.1 (pgs. 94-95): 3(d,g), 5 (Use the cofactor method for these.)
  4. Section 2.2 (p. 101): 2(a,b), 3(e,f), 4, 5, 6

• 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.
  1. 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.
  1. Section 3.2 (pgs. 131-132): 12(d,e), 16(a,b)
  2. Section 3.3 (pgs. 143-144): 2(c,e), 4(c), 10
  3. Section 3.4 (pgs. 149-150): 2(c,e), 13, 14(b,d)
  4. Section 3.6 (pgs. 165-166): 1(a,b), 3(a,b), 9, 14 (Note: a₁, a₂, a₃ a₄ 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.
  1. Section 3.5 (pg. 159): 3, 4, 6
  2. Find the transition matrix S_{E → F} if E = {1, x, x²} and F = {1-x, 2x+x², x²-1}
  3. In R², find the transition matrix S_{E → F} if E = {(1 -1)^T, (1 1)^T} and F = {(2 -1)^T, (1 2)^T}.
  4. Section 4.1 (pgs. 182-183): 4, 6(a,b,d), 10, 17(c), 19
  5. Section 4.2 (pgs. 195-196): 5(a), 15
  6. Let L : P₃ → P₃ be defined by L[p]= (2x² + x + 1)p'' − (3x − 1)p' + 2p.
     1. Show that L is linear.
     2. Find the matrix A of L relative to the standard basis E = {1, x, x²}.
     3. Find bases for the null space, and column space of A.
     4. Use the bases you found above to write down bases for the null space and image of L, in terms of polynomials.
     5. 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.
  1. Section 4.3 (pgs. 202-203): 4, 5(a,b,c), 6(a,b,c), 11
  2. Section 5.1 (pg. 225): 17, 18
  3. 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.
  1. Section 5.3 (pg. 243): 5(a), 7
  2. Section 5.5 (pg. 269-270): 1(b,c), 4, 15, 21(a,b(iii))
  3. 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.
  1. Section 10.2 (pg. 685): 10, 17
  2. Section 11.2 (pg. 739): 9(a), 14
  3. Section 11.3 (pg. 755): 4, 5

• These problems are for practice. We will discuss them in class. Don't turn them in.
  1. Section 11.3 (pg. 755-757): 18, 20
  2. Verify Stokes's Theorem in case F= 2yi + 3xj − z³k and S is the upper hemisphere of x² + y² + z² = 4, which has the circle x² + y² = 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)