Introduction to Matrices

In class today I gave an overview of how to use the sympy library to study matrices.

You can see a recording of the class here

Here is the notebook I used in class: matrices.ipynb

The matrix \(A\) is given by \(A=\begin{pmatrix}1 & 1 & a\\ 2 & a & 1\\ a & 1 & 2 a\end{pmatrix}\)

1. Find the determinant of \(A\).
2. Hence find the values of \(a\) for which \(A\) is singular.

3. For the following values of \(a\), when possible obtain \(A ^ {- 1}\) and confirm the result by computing \(AA^{-1}\):

   1. \(a = 0\);
   2. \(a = 1\);
   3. \(a = 2\);
   4. \(a = 3\).

Here is a recording of a summary I recorded during the 2020/2021 academic year: https://www.youtube.com/watch?v=rq_2ZYKq904. You might find that helpful.

I have now moved my personal teaching notes with plans on what I expect to do in each class. Note that you are not the target audience for these (I am) but I hope they’re helpful to you in your own note taking. There are links to each one on the page for each topic and you can find them all directly here https://vknight.org/cfm/class-notes/.

If you have any questions please let me know.