Assignment 1 - Due Thursday, May 31, 2012.

• Read sections 1.1-1.4 in the text. (My Notes on Row Reduction cover the essential material in 1.1 and 1.2.)
• Do the following problems.
  1. Use row reduction methods to solve the system S below. Put the solution in parametric form. Identify the leading and non leading variables. Find the solution to the corresponding homogeneous system. Again, put the solution in parametric form.

  2. Find the reduced row echelon form for the matrix B.

  3. For the matrices R, S, u, v, find the combinations below, if possible; if not, state why you can't.

     (a) 6R+3S

     (b) RT

     (c) RS

     (d) SR

     (e) vu

     (f) uv

     (g) Ru

     

Assignment 2 - Due Tuesday, June 5, 2012.

• Read sections 2.-2.3 and at least 3.1-3.3 in the text.
• Do the following problems.
  1. §1.3 (pp. 65): 10, 15
  2. §1.4 (pp. 76-79): 1(a,c), 3(a,b), 9(e,f,h), 14 (Hint for 14: use the "basic matrix trick" to rewrite the matrix in the form Ax = 0. What is x? Is it non zero?)
  3. §2.1 (pp. 105-107): 1(a,b,c), 4(b,d) (In 4, state the rule you used to get your answer.)

Assignment 3 - Due Thursday, June 7, 2012.

• Read sections 3.2-3.4 in the text.
• Do the following problems.
  1. §2.2 (pp. 112-115): 3(c,e,f), 4, 5 (Hint: What is the determinant of c·I, where I is the n×n identity?), 7, 10(b), 11.
  2. §2.3 (pp. 119-121): 1(c), 2(d) (Use the method of Example 3, p. 117)
  3. §3.1 (pp. 131-133): 16

Assignment 4 - Due Tuesday, June 12, 2012.

• Read sections 3.6, 4.1 in the text.
• Do the following problems.
  1. §3.2 (pp. 141-144): 2(a,b), 3(a,c,e), 6(a,b), 10(a,c), 14(b).
  2. §3.3 (pp. 154-156): 2(a,c,d), 6(b,c), 8.
  3. §3.4 (pp. 161-162): 2(a,c,d), 7, 14(a,d).
  4. §3.6 (pp. 180-183): 1(a,b), 2(a,b), 8.

Assignment 5 - Due Thursday, June 21, 2012.

• Read sections 4.2, 4.3, Change of Basis., 5.4 (skip "Norms" to end), 5.5 (up to p. 273).
• Do the following problems.
  1. §4.1 (pp. 195-198): 4, 8(b,c), 18(c).
  2. §4.2 (pp. 208-212): 4, 9(b(ii), 9(b(iii)), 12.
  3. §4.3 (pp. 217-219): 5, 6.

Assignment 6 - Due Monday, June 25, 2012.

• Read sections 5.5 (pp. 276-279), 6.1, 6.2 (2nd application), 6.3
• Do the following problems.
  1. §5.4 (pp. 267-270): 2, 7(b), 8(a,c).
  2. §5.5 (pp. 286-289): 2, 8, 9(a,b(ii)), 26.
  3. §6.1 (pp. 323-326): 1(c,d,g,h).
  4. §6.3 (pp. 351-355): 1(c,d), 2(c,d), 24(a,b)

Assignment 7 - Due Friday, June 29, 2012.

• Read sections 3.4, 6.1, 6.2, 7.1-7.3 in Part II.
• Do the following problems. (Problems are from Part II.)
  1. §6.1 (pp. 389-391): 9, 19
  2. §6.2 (pp. 398-400): 4, 10
  3. §7.1 (pp. 427-430): 4, 17

• Suggested problems -- not to be turned in.
  1. §6.1 (pp. 389-391): 10, 16, 18
  2. §6.2 (pp. 398-400): 6, 7, 8
  3. §7.1 (pp. 427-430): 2, 3, 5(c), 16
  4. §7.2 (pp. 448-449): 2, 3, 6, 10, 12, 20
  5. §7.3 (pp. 464-469): 2, 4, 5, 6, 8, 11, 12

Updated 6/28/2012 (fjn).