Linear Algebra in R³: Vector Spaces

This lecture covers the concept of vector spaces in three dimensions, exploring the definition of a family of vectors, linear combinations, and subspaces in R³. The instructor explains how to determine if a family of vectors is free or linked, and how to find the coordinates of a vector in a given basis. The lecture also delves into the properties of subspaces in R³, including the conditions for a set to be a subspace and the alternatives when a vector is part of a subspace. Examples and exercises are provided to illustrate the theoretical concepts.