The lecture notes (particularly the OCW video transcripts) offer three distinct advantages:
The row picture and column picture are two sides of the same coin. Solving (Ax = b) means finding the combination of columns of (A) that produces (b). lecture notes for linear algebra gilbert strang
Here is what you actually get when you hunt down these notes, and why they might be better than the textbook for your first pass. The lecture notes (particularly the OCW video transcripts)
Strang, however, shatters this mechanical view by introducing the "column picture." He posits that $Ax$ is not merely a calculation but a linear combination of the matrix’s columns. This shift is profound. Suddenly, the equation $Ax = b$ is no longer a set of $n$ equations with $n$ unknowns; it is a single geometric question: Can the vector $b$ be reached by combining the columns of $A$? lecture notes for linear algebra gilbert strang