Is It a Subspace? | The Subspace Test in Linear Algebra

In this Linear Algebra lesson, we introduce subspaces and learn how to determine whether a subset of a vector space is itself a vector space. Building on our previous lesson about vector spaces, we'll explore the conditions that a subset must satisfy to be a subspace and work through examples to see how these conditions are applied. Topics covered: What a subspace is The relationship between vector spaces and subspaces The zero vector requirement Closure under vector addition Closure under scalar multiplication Using the subspace test Determining whether a subset is a subspace Worked examples Understanding subspaces is an important step in Linear Algebra. These ideas provide the foundation for upcoming topics such as span, linear independence, bases, and dimension. Playlist: https://bit.ly/4qtJZ6r #linearalgebra #Subspaces #vectorspaces #SubspaceTest #vectors #collegemath #mathtutorial