{"id":1205,"date":"2017-08-21T16:04:19","date_gmt":"2017-08-21T20:04:19","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/jal\/?page_id=1205"},"modified":"2026-03-19T08:10:38","modified_gmt":"2026-03-19T12:10:38","slug":"homework-fall-2017","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/jal\/courses\/mas4105\/homework-fall-2017\/","title":{"rendered":"MAS 4105 Homework Fall 2017"},"content":{"rendered":"\r\n
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MAS 4105 Homework Fall 2017<\/h1>\n\n\n\n

Problems from Linear Algebra<\/em> by Friedberg, Insel, Spence<\/h4>\n\n\n\n
  • Monday, August 21: Read 1.1-1.2; do 1.2: 2, 3, 4, 10, 11, 13.
    \nMemorize the definition of vector space.
    \nRead Appendices A (sets) and B (functions).
    \nWhat is the definition of one-to-one? Onto?<\/li>\n
  • Tuesday,\u00a0August 22: Read 1.2; do 1.2: 1, 7, 9, 14, 15, 18.
    \nRead Appendix C (fields)<\/li>\n
  • Wednesday, August 23: Read 1.3; do 1.3: 2, 4, 5, 8, 10.<\/li>\n
  • Friday, August 25: Read 1.3; do 1.3: 11, 13, 23<\/li><\/ul>\n\n\n\n
    • Monday, August 28: Read 1.3-1.4; do 1.3: 1, 20, 23. 30<\/li>\n
    • Tuesday, August 29: Read 1.4; do 1.3, 20; 1.4: 2ace, 3ace, 4ace, 5ace
      \nFurther homework: Let V be the vector space R2<\/sup>.
      \n(a) Prove or disprove: the set of vectors (x,y) in V satisfying x=2y is a subspace.
      \n(b) Prove or disprove: the set of vectors (x,y) in V satisfying xy=0 is a subspace.<\/li>\n
    • Wednesday, August 30: Read 1.4; do 1.4: 1, 6, 9, 10, 13, 15<\/li>\n
    • Friday, September 1: Read 1.5 to bottom of page 38; do 1.5 2a-f, 3, 4, 7, 9, 10
      \nMemorize the definitions of linear independence and dependence
      <\/li><\/ul>\n\n\n\n
      • Monday, September 4: no class (Labor day)<\/li>\n
      • Tuesday, September 5: Read 1.5; do 1.5: 1, 12, 13q, 14, 19, 20<\/li>\n
      • Wednesday, September 6: Read 1.6; do 1.6: 2, 3, 4, 5, 6, 11<\/li>\n
      • Friday, September 8: <\/li><\/ul>\n\n\n\n
        • Monday, September 11: Hurricane Irma<\/li>\n
        • Tuesday, September 12: Hurricane Irma<\/li>\n
        • Wednesday, September 13: Hurricane Irma<\/li>\n
        • Friday, September 15: Read 1.6; do 6.1: 1, 7, 8, 13, 15, 17, 26<\/li><\/ul>\n\n\n\n
          • Monday, September 18: Basis and Dimension Perspective<\/li>\n
          • Tuesday, September 19: Homework Questions to Review for Exam 1<\/li>\n
          • Wednesday, September 20: (Exam 1 on 1.1-1.6) Read 2.1 through Example 1; do 2.1: 9<\/li>\n
          • Friday, September 22: Read 2.1; do 2.1: 7, 9, 12, 16\n<\/li><\/ul>\n\n\n\n
            • Monday, September 25: Read 2.1; do 2.1: 2-6<\/li>\n
            • Tuesday, September 26: Read 2.1; do 2.1: 12, 14a, 15, 18, 19<\/li>\n
            • Wednesday, September 27: Read 2.1; do 2.1: 1, 10, 11, 20, 38
              \n Suppose V<\/em> is a vector space of odd dimension.
              Describe the set of all linear transformations T: V -> V<\/em> such that R(T)=N(T)<\/em> <\/li>\n
            • Friday, September 29: Read 2.2; do 2.2: 2<\/li><\/ul>\n\n\n\n
              • Monday, October 2: Read 2.3; do 2.2: 3, 4, 5, 9, 10; 2.3: 2a<\/li>\n
              • Tuesday, October 3: Read 2.3; do 2.2: 1; 2.3: 2<\/li>\n
              • Wednesday, October 4: Read 2.3; do 2.3: 2, 3, 11<\/li>\n
              • Friday, October 6: Homecoming<\/li><\/ul>\n\n\n\n
                • Monday, October 9: Read 2.3; do 2.3: 4, 9, 12<\/li>\n
                • Tuesday, October 10: Read 2.4 to the bottom of page 100; do 2.4: 2, 3, 4, 6<\/li>\n
                • Wednesday, October 11: 1, 5, 7, 16, 17a<\/li>\n
                • Friday, October 13: Read 2.5; do 2.5: 2, 3ace; Start preparing for Exam 2 on 2.1-2.4 on Wednesday<\/li><\/ul>\n\n\n\n
                  • Monday, October 16: Read 2.5; do 2.5: 3ace, 4; prepare for Review for Exam 2 on 2.1-2.4<\/li>\n
                  • Tuesday, October 17: Read 2.5; do 5, 9; prepare for Exam 2 on Wednesday<\/li>\n
                  • Wednesday, October 18: Exam 2; Read 2.5: 5, 9<\/li>\n
                  • 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.<\/li><\/ul>\n\n\n\n
                    • Monday, October 23: Read 3.1-3.2; topic is rank; do 3.2: 2, 7<\/li>\n
                    • Tuesday, October 24: Read 3.2; topic is inverse of a matrix;

                      \nwritten homework due today; do 3.2: 5, and

                      \nHW problem: suppose $A$ is an m x n matrix. Prove that N(A) is a subset of N(A^tA) \n<\/li>
                    • Wednesday, October 25: Begin to read 3.3; topic: more on inverses; start systems of linear equations; do 3.2: 1, 6

                      \nHW 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.<\/li>\n
                    • Friday, October 27: Read 3.3 to page 176; do 3.3: 2, 3, 4; topic is systems of linear equations<\/li><\/ul>\n\n\n\n
                      • Monday, October 30: Read 3.3; Do 3.3: 1, 5, 7, 8, 10

                        \nHandout for Written Homework 2 due on Friday

                        \nExplain why, for an m x n matrix A with m =\/= n, either the column vectors or the row vectors are linearly dependent<\/li>\n
                      • Tuesday, October 31: Topic: Determinants; Read 4.4; do 4.4:2ac, 3aceg, 4aceg, 6.<\/li>\n
                      • 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.

                        \nTest 3 is next Wednesday; it Covers 2.4-2.5, 3.1-3.4, 4.4: 5, 6<\/li>\n
                      • 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<\/li><\/ul>\n\n\n\n
                        • Monday, November 6: 5.1; do 5.1: 4abfhij, 8<\/li>\n
                        • Tuesday, November 7: Review for Exam 3; do 5.1: 2, 3.<\/li>\n
                        • Wednesday, November 8: Exam 3<\/li>\n
                        • Friday, November 10: Veteran’s Day holiday<\/li><\/ul>\n\n\n\n
                          • Monday, November 13: Read 5.2; do 5.1: 12a, 14, 15a (use mathematical induction); 5.2: 2abc<\/li>\n
                          • Tuesday, November 14: Topic: Diagonalization; Read 5.2; do 5.2: 2, 7.<\/li>\n
                          • Wednesday, November 15: Topic: Inner product spaces; Read 6.1; <\/li>\n
                          • Friday, November 17:\n<\/li>
                          • Topic: Norms, orthogonal and orthonormal sets; Read 6.1, start 6.2; do 6.1: 10, 11, 17<\/li><\/ul>\n\n\n\n
                            • Monday, November 20: 6.2: Topics: Gram-Schmidt orthonormaliization algorithm, QR algorithm

                              \nRead 6.2; do 6.2: 2ac, 3; start Written Homework 3, due Wednesday, November 29; Takehome Quiz due Tuesday, November 28.<\/li>\n
                            • Tuesday, November 21: practice Gram-Schmidt, geometric aspects of projection, normalization<\/li>\n
                            • Wednesday, November 22: Thanksgiving holiday<\/li>\n
                            • Friday, November 24: Thanksgiving holiday<\/li><\/ul>\n\n\n\n
                              • Monday, November 27: Topics: Orthogonal bases, orthogonal complements

                                \nRead 6.2; do 6.2: 1, 5, and problems 1-2 on 6.1-6.2 exercises on canvas<\/li>\n
                              • 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<\/li>\n
                              • Wednesday, November 29 Topic: Least squares; four fundamental subspaces; Read 6.2: do problems 5-6 from 6.1-6.2 exercises on canvas<\/li>\n
                              • 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<\/li><\/ul>\n\n\n\n
                                • Monday, December 4: 6.2-6.3: do 8-9 from 6.1-6.2 exercises on canvas<\/li>\n
                                • Tuesday, December 5: Review for Exam 4 on 5.1 through end of class<\/li>\n
                                • Wednesday, December 6: Exam 4<\/li>\n
                                • Friday, December 8: Reading Day<\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":145,"featured_media":0,"parent":1159,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1205","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/1205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/users\/145"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/comments?post=1205"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/1205\/revisions"}],"predecessor-version":[{"id":1357,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/1205\/revisions\/1357"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/1159"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/media?parent=1205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}