Kicking off the linear algebra lessons, let's make sure we're all on the same page about how specifically to think about vectors in this context.

The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several vectors and adding them together.

Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.

Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.

What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions.