Solving a System of Linear Equations with a Matrix and Python

Here's how to solve a system of linear equations.

Google CoLab Python

Install Jupyter Notebooks

[brookestephen]

I began my python matrix project with a fraction class. It really helped!
I used key value pairs, where the "[row].[column]" is the key, like "0.0"

[alienmoonstalker]

I think you can use the @ symbol to do matrix multiply.

[BradleyG]

This can also be done with any scientific calculator that has matrix operations. For the TI-84, it’s under 2nd x⁻¹.
You can either enter M and b⃗ as two separate matrices and compute M⁻¹b⃗ with the built in operations, or you can put M and b⃗ as one adjoined matrix, where b⃗ is the final column. If you choose this method, you will then go to the bottom of the operators list and choose RREF, which will give you an adjoined matrix where M becomes an identity matrix, and the final column b⃗ becomes I⃗, which gives you your answers.

[Ketler]

Great. Would be great to see physical example of using Newton method for system of non-linear equations (use of Jacobian). 🎉

[BradleyG]

Edit: by ‘you’ I mean an interested reader, not you, Rhett.

I also highly recommend 3Blue1Brown’s Essence of Linear Algebra series if you find matrix operations to be arbitrary and view matrix solutions as a “neat trick”.

Understanding why matrices behave the way that they do becomes significantly easier once you understand the basic concept of a linear transformation, and visualizing makes understanding them even easier—hence why I recommend 3Blue1Brown.

Why this subject is not standard in an introduction to matrices in high school is infuriating, as it really does prevent you from understanding why matrices are useful for solving systems of equations.