HW 1:

Reading:
   Sections 1.1 through 1.5 and Appendices A through D as needed
Problems:
   1.2: 1, 9, 12, 13, 20
   1.3: 1, 5, 8, 23, 24, 30, 31
   1.4: 1; 2a-c; 3a; 4a; 5c, e, g; 6; 15
   Other Problems:
1. Prove that the real numbers are a vector space over the field of rational numbers, under the usual addition and with the usual multiplication as scalar multiplication.

HW 2:

Reading:
   Sections 1.5 through 1.7 and 2.1
Problems:
   1.5: 1*, 2c*, 2e*, 8, 13a
   1.6: 1*, 2a*, 3a*, 17, 33
   1.7: 1*
   2.1: 1*, 4, 5*, 9, 10, 13

HW 3:

Reading:
   Sections 2.2 through 2.4
Problems:
   2.2: 1*, 2a*, 2d*, 3*, 5b, 7, 11
   2.3: 1*, 2a*, 3a, 14a
   2.4: 1*, 4, 5

HW 4:

Reading:
   Sections 2.5 through 2.7
Problems:
   2.5: 1*, 2a*, 3e*, 6a*, 7a, 10
   2.6: 1*, 2*, 3a*, 5, 6
   2.7: 1*, 3e*, 6, 10, 13b

HW 5:

Reading:
   Sections 3.1 through 3.4
Problems:
   3.1: 1*, 7 (for the case of row operations only)
   3.2: 1*, 2a*, 2g*, 5e*, 6e, 21
   3.3: 1*, 2c*, 2g, 3c*, 3g, 4a*, 9
   3.4: 1*, 2a*, 2e, 3, 4c*, 5, 7*
   Other Problems:
1. Prove the following: If the augmented matirx (A|I) can be transformed into the augmented matrix (B|C) after a finite number of row operations then CA=B. Here I denotes the identity matrix and C is assumed to be the same size as I.
2. Using the matrix A from problem 4a of section 3.2, find the reduced row echelon form R of A and find a matrix C such that CA=R.

HW 6:

Reading:
   Sections 4.1 through 4.3
Problems:
   4.1: 1*, 2*, 3a, 3c*, 4c, 5, 7
   4.2: 1*, 2*, 3, 5*, 10, 25, 26
   4.3: 1*, 3*, 10, 11, 12*, 15

HW 7:

Reading:
   Sections 4.4, 4.5 and 5.1
Problems:
   4.4: 1*, 3f*
   4.5: 1*, 5*, 9*, 11 (corollary 2 only)
   5.1: 1*, 3a*, 3b, 3c, 5, 7, 8, 9*, 15

HW 8:

Reading:
   Sections 5.2, 6.1 and 6.2
Problems:
   5.2: 1*, 2e*, 2g*, 3d, 7, 8*, 11
   6.1: 1*, 2*, 6, 8, 10
   6.2: 1*, 2c*, 4, 9, 11*, 12

HW 9:

Reading:
   Sections 6.3 through 6.5
Problems:
   6.3: 1*, 2c, 3b, 8, 10
   6.4: 1*, 2c, 4, 17a
   6.5: 1*, 11, 24

HW 10:

Reading:
   Sections 6.11, 6.6 and 6.8
Problems:
   6.11: 1*, 6, 11
   6.6: 1*, 4
   6.8: 1*, 2, 3*, 5b, 16, 17a, 25@

@ Note on problem 25: There is an easier way to do this problem without the hint given in the book. Here is a better hint: For each fixed y, use theorem 6.8 to define T as a funtion. Then show T is linear. This is the same idea as the proof of theorem 6.9. (This problem is required.)

HW 11:

Reading:
   Sections 7.1 and 7.2, and skim 7.3 and 7.4
Problems:
   7.1: 1*, 2c, 3a, 4, 7a-d
   7.2: 1*, 2*, 3, 4a, 6
   7.3: 1*, 2*, 5*
   7.4: 2a*


* Starred problems are optional. They do not have to be handed in but it is strongly recommended that you know how to do these problems.

Be sure to check all your answers in the back of the book when possible.