Introduction to Linear Algebra is a course by Gilbert Strang for MIT
When we look at equations, we have a few different perspectives
3x + 2y = 4 -x + 2y = 3
We can visualise it as the following forms
This is when we try to rewrite it in the original form that we learnt in school
We can also visualise it as a linear combination of vectors
All three are equally valid ways of visualising the problem but when we get to higher dimensions, the row and column views start to be a bit more limited in their usage since it gets difficult to visualise.
If all vectors are within the same plane, then we cannot discover a unique vector that is an answer to the solution