You might want to watch this short video a couple of times - https://www.youtube.com/watch?v=rowWM-MijXU https://www.youtube.com/watch?v=rowWM-MijXU A simple w

You might want to watch this short video a couple of times - https://www.youtube.com/watch?v=rowWM-MijXU https://www.youtube.com/watch?v=rowWM-MijXU A simple way to think about Linear Algebra is as a set of rules i.e. functions (aka Matrices) applied to input points (aka vectors) to give output points in a vector (i.e. multidimensional) space. Thus multi-valued inputs give multi-valued outputs. The key is to keep both the algebraic manipulations and what they may mean in the geometric interpretation simultaneously in mind. The basic example of solving a system of linear equations in two variables will cement this idea when you map it to the XY coordinate system. You might find the book Practical Linear Algebra : A Geometry Toolbox by Farin and Hansford useful for further study.