Vector Subspaces and Subspace Test Explained | Linear Algebra
If V is a vector space and W is a subset of V, then W may itself be a vector space and if so is called a subspace, or linear subspace, of the vector space V. We introduce the definition of a vector subspace, the subspace test, see a proof of the subspace test, and then we'll look at several examples of subspaces and non-examples of subspaces in R^2, R^3, Mnn and more. #linearalgebra
Using the Subspace Test: • Prove the Set is a Subspace with Subs...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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0:00 Intro
0:38 Definition of a Vector Subspace
2:23 Nontrivial Subspace Properties
4:10 Subspace Test
7:38 Trivial Subspaces
9:04 Subspaces of R^2 and R^3
11:08 Non-Examples of Subspaces in R^2 and R^3
12:29 Subspaces of Square Matrices
13:50 Non-Examples of Subspaces of Square Matrices
14:27 Conclusion
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