## MAT223 Linear Algebra Exam Review questions answered in videos

Dear students from MAT223:

I’ve received some requests to explain the following questions and I made a few short videos to explain how to solve them.

Happy learning!

1. If and are linear transformations , and are three distinct vectors in so that

then for all

2. If A is matrix and dim(null(A-I))=3, then A is diagonalizable.

3. Consider

4. What is the matrix of a linear transformation

with

Compute the rank of this matrix.

## 2019 Winter MAT102: Intro to Math Proof

The main topics that we cover in this course are:

1. Numbers, and Inequalities.
2. Sets, functions and fields.
3. Informal logic.
4. Mathematical Induction.
5. Bijections and cardinality.
6. Integers and divisibility.
7. Relations.

The course note is available: MAT102

The slides for weekly lectures can be found here:

Below are a few short video clips I made to explain certain questions upon students’ request.

1. 2.5.29 Part a) Prove or disprove if two functions f and g are bounded, then their sum f+g is bounded.
2. 2.5.29 Part b). Prove of disprove if two functions f and g are bounded, then f^2-g^2 is bounded.
3. 2.5.50. Show that in any field F, the equation x^2 = 1 can have at most two solutions.
Can you think of a field in which the equation x^2 = 1 has exactly one solution?