Homework for Math 342; Linear Algebra II

 

 

·        1/5             Prove Theorem 1c from class: Let V be the set of all eigenvectors of an nxn  matrix A with zero vector added. Show that V is a linear subspace of Rn.

                         5.1:  2, 6, 10, 16, 24, 27, 31

·        1/6             Prove Theorem 4c from class: Similar matrices have the same characteristic equations.

                         5.2:  2, 4, 6, 8, 10, 14, 17, 20, 21

·        1/7               5.3:  2, 10, 14, 18, 23, 24

·        1/9              5.3:  3, 6, 15, 17, 21, 22

                         Review linear transformations and how to construct a matrix of a linear transformation: 1.8, 1.9

 

                  HW 1 due Wed., Jan. 14

___________________________________________________________________________________________________________________________

 

·        1/12           No homework

·        1/14           5.4:  3, 4, 5, 7, 11, 12, 13, 16, 17, 20, 22, 29

      ·        1/16           5.4:  1, 10, 14

 

                  HW 2 due Wed., Jan. 21

___________________________________________________________________________________________________________________________

 

·        1/19           No class

·        1/21           5.5:  1, 2, 5, 6;

                        Supplementary exercises to Ch. 5:  17 (p.372)

                        Review complex numbers: Appendix B

      ·        1/23           5.5:  7, 8, 9, 10, 11, 12, 13, 14, 15, 16

 

 

                  HW 3 due Wed., Jan. 28

___________________________________________________________________________________________________________________________

 

·        1/26           5.6:  1, 5

            ·        1/28           5.6:  7, 9, 10, 11, 12

      ·        1/30           6.1:  1-8

 

                  HW 4 due Wed., Feb. 4

___________________________________________________________________________________________________________________________

 

·        2/2             Prove part 1 of Theorem 15c from class: Let W be a subspace of Rn. Prove that the orthogonal complement of W is also a subspace of   Rn.

                        6.1: 10, 13, 14, 16, 17,  24, 25, 31

·        2/4             6.2:  1, 4, 5, 7, 8, 10, 17, 18, 20, 21, 22, 26

·        2/6             6.2:  11-16, 23, 24, 33

 

 

                  HW 5 due Wed., Feb. 11

___________________________________________________________________________________________________________________________

 

·        2/9             Review.  No homework.

·        2/11           6.2:  27, 29, 30

                        6.3:  1, 3, 4, 7, 8, 9, 17

·        2/13           6.3:  11-15, 18-23      

 

 

                  HW 6  due Wed., Feb. 18

___________________________________________________________________________________________________________________________

 

·        2/16           6.4:1,2,3,6,8,9,12,13,16,17,18.

·        2/18           6.5:3, 4, 5, 7, 8, 9, 12, 13, 15, 16, 17, 24, 25

·        2/20           No homework assigned

 

HW 7  due Wed., Feb. 25

 

___________________________________________________________________________________________________________________________

 

·        2/23           6.7: 3-6, 13, 16, 18, 20

·        2/25           6.7: 7-12

·        2/27           7.1: 2, 4, 6, 8, 10, 13, 16, 17, 18, 22, 24, 27, 28, 29

 

HW 8  due Wed., Mar. 2

 

___________________________________________________________________________________________________________________________

 

·        3/1             7.2: 1-6

·        3/3             7.2: 8, 7

·        3/5             7.2: 9-14, 19, 20, 23, 24

 

Homework assignment will NOT be collected this week.