Problems from Linear Algebra by Friedberg, Insel, Spence
Monday, August 21: Read 1.1-1.2; do 1.2: 2, 3, 4, 10, 11, 13.
Memorize the definition of vector space.
Read Appendices A (sets) and B (functions).
What is the definition of one-to-one? Onto?
Tuesday, August 22: Read 1.2; do 1.2: 1, 7, 9, 14, 15, 18.
Read Appendix C (fields)
Wednesday, August 23: Read 1.3; do 1.3: 2, 4, 5, 8, 10.
Friday, August 25: Read 1.3; do 1.3: 11, 13, 23
Monday, August 28: Read 1.3-1.4; do 1.3: 1, 20, 23. 30
Tuesday, August 29: Read 1.4; do 1.3, 20; 1.4: 2ace, 3ace, 4ace, 5ace
Further homework: Let V be the vector space R2.
(a) Prove or disprove: the set of vectors (x,y) in V satisfying x=2y is a subspace.
(b) Prove or disprove: the set of vectors (x,y) in V satisfying xy=0 is a subspace.
Wednesday, August 30: Read 1.4; do 1.4: 1, 6, 9, 10, 13, 15
Friday, September 1: Read 1.5 to bottom of page 38; do 1.5 2a-f, 3, 4, 7, 9, 10
Memorize the definitions of linear independence and dependence
Monday, September 4: no class (Labor day)
Tuesday, September 5: Read 1.5; do 1.5: 1, 12, 13q, 14, 19, 20
Wednesday, September 6: Read 1.6; do 1.6: 2, 3, 4, 5, 6, 11
Friday, September 8:
Monday, September 11: Hurricane Irma
Tuesday, September 12: Hurricane Irma
Wednesday, September 13: Hurricane Irma
Friday, September 15: Read 1.6; do 6.1: 1, 7, 8, 13, 15, 17, 26
Monday, September 18: Basis and Dimension Perspective
Tuesday, September 19: Homework Questions to Review for Exam 1
Wednesday, September 20: (Exam 1 on 1.1-1.6) Read 2.1 through Example 1; do 2.1: 9
Friday, September 22: Read 2.1; do 2.1: 7, 9, 12, 16
Monday, September 25: Read 2.1; do 2.1: 2-6
Tuesday, September 26: Read 2.1; do 2.1: 12, 14a, 15, 18, 19
Wednesday, September 27: Read 2.1; do 2.1: 1, 10, 11, 20, 38
Suppose V is a vector space of odd dimension. Describe the set of all linear transformations T: V -> V such that R(T)=N(T)
Friday, September 29: Read 2.2; do 2.2: 2
Monday, October 2: Read 2.3; do 2.2: 3, 4, 5, 9, 10; 2.3: 2a
Tuesday, October 3: Read 2.3; do 2.2: 1; 2.3: 2
Wednesday, October 4: Read 2.3; do 2.3: 2, 3, 11
Friday, October 6: Homecoming
Monday, October 9: Read 2.3; do 2.3: 4, 9, 12
Tuesday, October 10: Read 2.4 to the bottom of page 100; do 2.4: 2, 3, 4, 6
Wednesday, October 11: 1, 5, 7, 16, 17a
Friday, October 13: Read 2.5; do 2.5: 2, 3ace; Start preparing for Exam 2 on 2.1-2.4 on Wednesday
Monday, October 16: Read 2.5; do 2.5: 3ace, 4; prepare for Review for Exam 2 on 2.1-2.4
Tuesday, October 17: Read 2.5; do 5, 9; prepare for Exam 2 on Wednesday
Wednesday, October 18: Exam 2; Read 2.5: 5, 9
Friday, October 20: Read 3.1-3.2; do 3.1: 1, 2, 3; look for written homework due Tuesday at the beginning of class. You must work alone on this homework.
Monday, October 23: Read 3.1-3.2; topic is rank; do 3.2: 2, 7
Tuesday, October 24: Read 3.2; topic is inverse of a matrix;
written homework due today; do 3.2: 5, and
HW problem: suppose $A$ is an m x n matrix. Prove that N(A) is a subset of N(A^tA)
Wednesday, October 25: Begin to read 3.3; topic: more on inverses; start systems of linear equations; do 3.2: 1, 6
HW problem: Let A be an m x n matrix, m not equal to n. Explain why either the row vectors or the column vectors are linearly dependent.
Friday, October 27: Read 3.3 to page 176; do 3.3: 2, 3, 4; topic is systems of linear equations
Monday, October 30: Read 3.3; Do 3.3: 1, 5, 7, 8, 10
Handout for Written Homework 2 due on Friday
Explain why, for an m x n matrix A with m =/= n, either the column vectors or the row vectors are linearly dependent
Tuesday, October 31: Topic: Determinants; Read 4.4; do 4.4:2ac, 3aceg, 4aceg, 6.
Wednesday, November 1: Read 3.4: do 3.4: 2, 4, 7, 8; prepare to turn in written homework 2 on Friday at the beginning of class.
Test 3 is next Wednesday; it Covers 2.4-2.5, 3.1-3.4, 4.4: 5, 6
Friday, November 3: Turn in Written Homework 2 at the beginning of class; Read 5.1; do: 5.1: 2, 3 3.4: 1, 10, 12
Monday, November 6: 5.1; do 5.1: 4abfhij, 8
Tuesday, November 7: Review for Exam 3; do 5.1: 2, 3.
Wednesday, November 8: Exam 3
Friday, November 10: Veteran’s Day holiday
Monday, November 13: Read 5.2; do 5.1: 12a, 14, 15a (use mathematical induction); 5.2: 2abc
Tuesday, November 14: Topic: Diagonalization; Read 5.2; do 5.2: 2, 7.
Wednesday, November 15: Topic: Inner product spaces; Read 6.1;
Friday, November 17:
Topic: Norms, orthogonal and orthonormal sets; Read 6.1, start 6.2; do 6.1: 10, 11, 17
Monday, November 20: 6.2: Topics: Gram-Schmidt orthonormaliization algorithm, QR algorithm
Read 6.2; do 6.2: 2ac, 3; start Written Homework 3, due Wednesday, November 29; Takehome Quiz due Tuesday, November 28.
Tuesday, November 21: practice Gram-Schmidt, geometric aspects of projection, normalization
Wednesday, November 22: Thanksgiving holiday
Friday, November 24: Thanksgiving holiday
Monday, November 27: Topics: Orthogonal bases, orthogonal complements
Read 6.2; do 6.2: 1, 5, and problems 1-2 on 6.1-6.2 exercises on canvas
Tuesday, November 28: Topic: Orthogonal projection; Read 6.2; do 6.2: 19, 20, and 3, 4 from 6.1-6.2 exercises on canvas
Wednesday, November 29 Topic: Least squares; four fundamental subspaces; Read 6.2: do problems 5-6 from 6.1-6.2 exercises on canvas
Friday, December 1: Topic: Least squares; glance at 6.3; do 6.3: 20a, 20b (linear approximation only), and do problems 7-8 from 6.1-6.2 exercises on canvas
Monday, December 4: 6.2-6.3: do 8-9 from 6.1-6.2 exercises on canvas
Tuesday, December 5: Review for Exam 4 on 5.1 through end of class