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

Matrix Form

Row Form

This is when we try to rewrite it in the original form that we learnt in school

Column View

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