MAS4105 Homework
On this page you will find the weekly homework assignments for
Linear Algebra I.
The following homework assignments refer to the course text book, section
numbers and exercise numbers.

Jan 7, prepare until Jan 14
Section 1.2: Ex. 1 (except (e)), 2, 3, 4, 8, 12
Section 1.3: Ex. 1 (except (f)), 8, 12, 15

Jan 14, prepare until Jan 21
Section 1.4: Ex. 1 (a)(c) (the others if you like), 11, 12, 14, 15 (note
that you can use the theorems from the lectures)
Section 1.5: Ex. 1, at least one of {4, 5, 6}, 9, 10, 16, 18

Jan 21, prepare until Jan 28
Section 1.6: Ex. 1, 2, 4, 6, 11, 13, 29(a), 35

Jan 31, prepare until Feb 4
Consider matrices in 3.2, Exercise 2 (a),(b),(c),(f),(g). Compute all
products of them which are defined. For each of the matrices compute bases
of its row space and its column space.

Feb 5, prepare until Feb 11
 Prove Remark (4.6) from the lecture.
 Prove Theorem (4.7)(b) from the lecture.
 Consider the systems of linear equations printed in the textbook,
Section 3.3, Exercises 2 and 3 parts (a),(c),(e),(g). Show that the sets of
solution in Exercise 2 are subspaces of the space of ktuples over the real
numbers (for appropriate k). What is the relations between the sets of
solutions for the systems in Exercise 3 and the corresponding system in
Exercise 2?

Feb 12, prepare until Feb 18
Section 3.1: Ex. 1 (the term "elementary matrix" means one of the matrices E
from (4.15) in the lecture), 2, 4
Section 3.2: Ex. 1, choose a few of 2 and 5, 17

Mar 5, prepare until Mar 18
Section 2.1: Ex.1 (without (e)), 2, 3, 4, 5, 6, 18, 19, 20

Mar 18, prepare until Apr 1
Section 2.2: Ex. 1, 2, 4, 16

Apr 2, prepare until Apr 8
Section 2.3: Ex. 1 (a)(d), 3, 12
Section 2.4: Ex. 1 (not (c), (h)), 2, 3, 14

Apr 9, prepare until Apr 15
Section 2.5: Ex. 1, 2, 5
Section 4.4: Ex. 1, 5, and some of Ex. 2 and 3 and 4
Section 4.5: Ex. 1, 16