Vector Spaces in R2 and R3

This lecture covers the intersection of vector planes in R3, proving that two vector planes are proportional, and determining the intersection of two vector planes. It also explains how to describe the intersection of two vector planes using equations. The lecture further explores how to identify proportional vectors and bases in IR3, as well as the concept of canonical bases. The instructor demonstrates how to calculate the change of base matrix from one basis to another and provides examples of vector decompositions and coordinate transformations.