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.
If and are linear transformations , and are three distinct vectors in so that
2. If A is
matrix and dim(null(A-I))=3, then A is diagonalizable.
Decide whether A is diagonalizable. Justify your answer.
4. What is the matrix of a linear transformation
Compute the rank of this matrix.
The main topics that we cover in this course are:
Numbers, and Inequalities. Sets, functions and fields. Informal logic. Mathematical Induction. Bijections and cardinality. Integers and divisibility. Relations.
The course note is available:
The slides for weekly lectures can be found here:
MAT102_Week1-2 MAT102_Week2-3 MAT102_Week 4-5 MAT102_Week 6 MAT102_Week 7 MAT102_Week 8 MAT102_Week 9 MAT102_Week10 MAT102_Week 11-12
Below are a few short video clips I made to explain certain questions upon students’ request.
2.5.29 Part a) Prove or disprove if two functions f and g are bounded, then their sum f+g is bounded. 2.5.29 Part b). Prove of disprove if two functions f and g are bounded, then f^2-g^2 is bounded. 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?