Summer of Math Exposition

Clear explanation of how to find the determinate of matrices.

I would have liked to see at what size matrix cofactor expansion becomes more work than using row operations to help students choose the fastest method for their problem. Your example, for solving linear equations using Cramer’s rule will appear significantly more complicated to students than their existing method for solving simultaneous equations. I think an example showing how to calculate the area of a triangle using the determinate would highlight the importance of the determinate more.

The question for why should we use and learn matrices has not been answered. My answer is it easy to tell a computer how to do perform the calculations for us. The data structure of a matrix is such that operations can be performed in the exact same way every time. Programing the substitution method to solve linear equations would be significantly more work and run slower. Further a computer is always going to be faster than a person.

This appears to be a standard textbook rendition of the topic, with no new insights.

It was a comprehensive guide to calculating the determinants and there were clear examples. It would definitely be useful. I would have liked to see some explanation as to why the formula gives the area of the transformation, or some other visualisation to depict what is happening when we calculate the determinant

Very clear explanations. Some geometrical visualisations could be nice.

The “What is a Determinant” section is probably the most engaging. Gives the reader a sense of why they should care about the mathematical operation