# Math 4326 Linear Algebra Homework

## Dr. Duval

### Discussion items

1.2: Thm. 1; Ex. 4-6; Prop. 2; Ex. 8-11, 13.
1.3: Prop. 1-3; Ex. 1,3,4; Prop. 4; Prop. 6/Ex. 6; Prop. 7.
1.4: Ex. 7; Lemma 1; Thm. 2; Ex. 8-10; Cor. 3; Lemmas 4, 5; Thm. 6, Ex. 14; Thms. 7-8; Thm. 9; Ex. 18/20.
1.5: Thm. 2; Exercise 1.5.6 (p. 71); Ex. 7-8; Props 3-4; Prop. 5; Ex. 11.

2.1: Exercise 2.1.5 (p. 71); Prop. 2; Prop. 3; Ex. 13-14.
2.2: Rank and Nullity Thm; Thm. 2; Exercise 2.2.20 (p. 90); Thm. 3; Thm. 6; Exercises 2.2.7, 2.2.2.ii, 2.2.3.ii (p. 88).
2.3: Props. 1, 2; Thm. 3; Ex. 3; Thm. 5; Ex. 7; Thm. 6; Ex. 10.

3.1: Exs. 2b, 2c; Exercise 3.1.13.
3.2: Thm. 1; Lemma 2; Thm. 3; Exercise 3.2.5(b); QR Thm.; Exercise 3.2.6(c).
3.3: Thms. 1, 3; Ex. 3; Thm. 6; Thm.7; Exercise 3.3.6.

4.1: Prop. 1; Exercise 4.1.7 (f maps reals to reals); Prop. 3/Cor. 4; Exercise 4.1.11.
4.2: Thm. 3; Thms. 5, 6; Excercise 4.2.6.
4.3: Thm. 2; Excercise 4.3.4; Thm. 4.

### Homework problems (to turn in)

Homework 1: 1.1.1ab, 1.2.7, 1.2.10.
Homework 2: 1.3.10, 1.3.21, 1.4.5.
Homework 3: 1.4.10, 1.4.29, 1.4.36.
Homework 4: 1.5.6, 2.1.7, 2.1.9.
Homework 5: 2.2.14, 2.2.17, 2.3.10.
Homework 6: 3.1.11, 3.2.26, 3.3.2.