Spreadsheet Math: Making a Matrix Calculator
With unit 2 focusing mostly on systems of equations, which can be annoyingly tedious to solve, I decided to have my students create a calculator using a spreadsheet that can solve systems of equations using matrix methods.
Creating this mathematical model helps students not only reinforce their understanding of mathematical concepts (finding the determinant, inverse, sum, and product of matrices), but also teaches them to
- use reference cells to execute calculations based on variable inputs
- share link and manage permissions
For this project I require their calculator to be able to do the following
- add two matrices together
- multiply two matrices
- calculate the determinant
- produce the inverse of the matrix
- solve a system of equations
- do all of the above for both [2x2] and [3x3] matrices/systems
Because I want to check that their calculator actually works, I have the students submit this task by sharing its link. I also require that they grant editing privileges to me so I can change the inputs and observe the resulting outputs myself.
Overall, this project is fairly straightforward and simple (i.e. here’s a checklist, complete it). Once students create their first matrices A and B and begin working out a new matrix that either adds or multiplies A and B together, they seem to do pretty well on their own -at least until it comes time to finding the inverse of a 3x3 matrix.
Because finding the inverse of a 3x3 matrix (and then using it to solve a 3D system of equations) is actually beyond the scope of this class, I do not teach it in class. However, with a little bit of help from Google, it is still very achievable, as was the case for the overwhelming majority of my students.
As you can see below, students get pretty creative with presentation as well -especially after they discover how to change font and background colors.
