# Math 1021, Linear Algebra 1, Sections A and B. Ilijas Farah, Fall 2017.

### Suggested exercises

These exercises range from straightforward computations to fairly nontrivial theorems that will eventually be covered in class. It is strongly recommended that you think about all exercises and work out some of the computations. It is strongly recommended not to read the solutions to the exercises prior to thinking about them hard enough to solve some of them. If you find yourself reading most of the solutions and solving very few exercises, then you are not preparing for the tests and the exams. If you are having difficulties with the material, contact me or go to Math Lab, Ross S525. Once the semester is under way teaching assistants will be available in this room during the working hours). Some of the exercises are starred (like this: 1*). These are theoretical exercises that may sometimes sound as if they have little to do with the material taught in class, but they do. It is up to you to discover the connections. (Technically speaking, students who expect to merely pass the course need not lose their sleep over these exercises. However, doing so will turn beautiful mathematics into a chore and rob you of most of the benefits of taking this course.) Suggested exercises
1.1, Solutions and elementary operations
4-8, 12, 15, 17, 18
1.2, Gaussian elimination
1,2, 5-11, 12*, 13-16
1.3 Homogeneous equations
1-3, 5,6,7*, 8-10?
2.1 Matrix addition, scalar multiplication, and transposition
1-5, 8, 9*, 10-21
2.2 Equations, matrices, and transformations
1-7, 9,10,12,13*,14,16-18,20,21
2.3 Matrix multiplication
1-4,6-21,23,24,27,28*,29*,30*,31*,32-34
2.4 Matrix inverses
1,2,3ab,4ac,5ab,8-12,14,17-21,24-28,30-34,36,37,39,41
2.5 Elementary matrices
1-4,6,8,9,12-14,16,17ab,18,21,22
2.6 Linear transformations
1,3-7,9,11-18,20-23
2.7 LU-factorization
1-4,5*,6*,9
Suggested exercises from sections 3.1-3.4, 4.1-4.4, 5.1-5.6 will be posted soon.
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