MATH 221: Linear Algebra and Applications
Section 04 (Fall 2013)

List of the homework problems and the due dates

Multiple-page homework should be stapled.

Assignments are due at the beginning of the class on the indicated due date.

Linear Algebra: A geometric approach (Shifrin and Adams), 2nd Edition

• Homework assignment 1 (Due on September 5, in class)
  1.1, Vectors: pp. 15-18: 6(a,c,g), 7, 8, 10, 11, 21, 22, 23, 25, 29
  1.2, Dot products: pp. 25-28: 1(b,d,g), 2(b,d,g), 4, 9, 11, 13 (no geometric interpretation necessary), 16, 18

• Homework assignment 2 (Due on September 12, in class)
  1.3, Hyperplanes in R^n: pp. 34-35: 1(a,c,f), 3(a,d,e), 5, 8, 10, 12
  1.4, Linear systems: pp. 49-53: 1, 3(a--f), 4(d,f), 10, 11, 13

• Homework assignment 3 (Due on September 19, in class)
  1.5, Theory of linear systems: pp. 61-64: 1, 2(a,b), 3(a,c), 4a 5b, 6, 10, 12, 13, 14
  1.6, Some applications: pp. 75-77: 3, 5, 7, 9, 11, 12a, 13b
  2.1, Matrix operations: pp. 89-91: 1(a, c, f), 2, 5, 6, 7, 8, 9, 12 (a, b, d), 14

• Homework assignment 4 (Due on September 26, in class)
  2.2, Linear transformations: pp. 100-102: 5, 7, 8
  2.3, Inverse matrices: pp. 108-110: 1(b, d, f), 2(a, c, d), 4, 8, 11, 12, 16
  2.4, Elementary matrices: pp. 118-119: 3(a,c,d), 7, 14

• Homework assignment 5 (Due on October 8, in class)
  2.5, Transpose matrices: pp. 122-124: 1(a, f, j), 4, 8, 9, 12, 15, 19(a, b,c), 22, 23
  3.1, Subspaces of R^n: pp. 134-135: 1, 2(a, c, d), 6, 9(b,c), 10, 12, 13, 17
  3.2, The four fundamental subspaces: pp. 142-143: 2(a,b), 5, 10, 11

• Homework assignment 6 (Due on Ocotber 24, in class)
  3.3, Linear independence: pp. 154-156: 1, 2, 5(a, b), 8, 10, 11, 14, 15, 19, 21, 22
  3.4, Dimension: pp. 167-170: 2, 3(a,b,d), 4, 7, 17, 20, 24
  3.6, Abstract vector spaces: pp. 185-188: 1, 2(a,c,d), 3(a,c,f), 4, 6(a,b), 9, 12a, 13, 14(b,c), 15(a,b)
  

• Homework assignment 7 (Due on Oct 31, in class)
  4.1, Inconsistent systems and projection: pp. 198-200: 1(a,b), 3, 6, 7, 9, 11, 13, 15
  4.2, Orthogonal bases: pp. 206-208: 2(b,c), 3, 6, 7(a,b), 8a, 9a, 11, 12(a,b)

• Homework assignemtn 8 (Due on Nov 7, in class)
  4.3, The matrix linear transformation: pp. 220-224: 3, 7, 9, 12, 16, 18, 19, 20, 21
  4.4, Abstract linear transformation: pp. 234-237: 2, 5, 7, 8, 11, 21

• Homework assignment 9 (Due on Nov 14, in class)
  5.1, Determinants: pp. 243-245: 1(a,b,c), 2, 3, 4, 7, 9a, 10, 11
  5.2, Cofactors and Cramer's rule: pp. 252-255: 1a, 3, 4, 5(a,c,f) 7, 8, 10
  5.3, Signed area and volumes: pp. 258-260: 3, 5, 7

• Homework assignment 10 (Due on Nov 21, in class)
  6.1, The characteristic polynomial: pp. 268-270: 1(a,d,g,i), 2, 3, 4, 6, 7(a,d), 9, 10, 13(a,b)
  6.2, Diagonalizability: pp. 274-277: 1(a,d,g,i), 2(c,f), 4, 7, 8, 11, 12, 13, 15, 17a, 19(a,b)

• Homework assignment 11 (Due on Dec 5, in class)
  6.4, The spectral theorem: pp. 294-296: 1(a,d,e,g), 3, 5, 7, 12(a,b,c,d), 14
  7.1, Complex eigenvalues and Jordan Canonical Form: pp. 312-314: 1, 2(a,b,c,e), 4,5, 7(a, b,c), 8(a,c,e), 14, 16

Last Modified November 26 (Tuesday), 2013.