This page is dedicated to Shaheed Bibi Paramjit Kaur.
Linear Algebra Step by Step – the URL of the book is
Complete solutions to all exercises in the book are here:
Topic Videos and Test Questions
All the test questions below were developed by Dr Martin Greenhow and his team at Brunel University London. (You can enter any name and any number like 123 for your student number. Also don’t need to give your email address, just enter a school where it asks for your email address.) You can do the test as many times as you wish as the numbers change every time you refresh the page.
There are also test questions from Newcastle University using Numbas and these were developed by Bill Foster and Christian Perfect.
Notes on Mathematical Induction
Chapter 1 Linear Equations and Matrices
Chapter 2 Euclidean Space
Notes for section 2,2 are here
Notes for section 2.3 are here
Chapter 3 General Vector Spaces
Here are the notes for section 3.1
Here are the notes for section 3.2
Here are the notes for section 3.3
Here are the notes for section 3.4
Here are the notes for section 3.5
Notes for section 3.6 are here
chapter 4 Inner product spaces
Notes on section 4.1 are here
chapter 6 Determinants and the inverse matrix
Chapter 7 Eigenvalues and eigenvectors
Online test on eigenvalues and eigenvectors of 3 by 3 matrices Test on Properties of Eigenvalues and Eigenvectors - Section 7.2
Supplementary Problems with Brief Solutions are at the following link:
If you are an academic and would like complete solutions to these problems then email me at firstname.lastname@example.org
Challenging Problems on Linear Algebra with complete solutions are Here
Applications of Linear Algebra
SVD application by Becky Wheeler is here
Below is a set of supplementary notes on Linear Algebra.
Notes on Proof by Mathematical Induction.
Introductory CHAPTER: Mathematical Logic, Proof, and Sets
|Section A: Joy of Sets
|Section A||Exercise Ia||Complete Solutions to Exercise Ia|
|Section B: Subsets (Video)
Section B: Power Set Video
|SECTION B Subsets||Exercise I (b)||Complete Solutions to Exercise I(b)|
|Section C: Proposition Logic
|Section I(c)||Exercise I(c)|
|Section D: Algebra of Propositions
Video of lecture
|Section I(d)||Exercise I(d)||Complete solutions to Exercise I(d)|
|Section E: Implication
Video of lecture
On the following test enter your truth values in numerical order.
|Exercise I(e)||Complete solutions to Exercise I(e)|
|Section F: Introduction to Proof
|Section I(f)||Exercise I(f)||Complete solutions to Exercise I(f)|
|Section G: Proofs
|SECTION I(g) PROOFS||Exercise I(g)|
|Section H: Proof by Contradiction
|SECTION I(h) PROOF BY CONTRADICTION||Exercise I(h)||Complete Solutions to Exercise I(h)|
|Section I: Principle of Mathematical Induction||Section I(i)||Exercise I(i)||Complete Solutions to Exercise I(i)|
Chapter 6: Determinants
Chapter 7: Eigenvalues and Eigenvectors
Demonstration of eigenvalue and eigenvector here
Harish Chandra 1923 to 1983
In mathematics, there is an empty canvas before you, which can be filled without reference to external reality.
Mathematicians on Creativity by Peter Borwein
Hermann Schubert (1848 to 1911)
â€œâ€¦ the three positive characteristics that distinguish mathematical knowledge from other knowledge â€¦ may be briefly expressed as follows; first, mathematical knowledge bears more distinctly the imprint of truth on all its results than any other kind of knowledge; secondly, it is always a sure preliminary step to the attainment of other correct knowledge; thirdly, it has no need of other knowledge.â€
Hermann Schubert in ‘Mathematical Essays and Recreations’ 1898
This is a direct quote from ‘Mathematicians on Creativity by Peter Borwein
Test and Examination Papers in Linear Algebra
A good way to revise for examination is to try past examination papers. It is important that you attempt the paper without looking at the solutions. Even if you get stuck, it is better to have a go at the question and then at the end mark your paper. This is a much more effective way of learning because you will have an understanding of the material and now what is required of you. Of course, this is much harder but also more rewarding.
Linear Algebra web links:
The following video explains why linear algebra is important.
The following is a fantastic source of videos on linear algebra. Please check it out.