Linear Algebra Lecture 23 | Extending and Shrinking a Set to Form a Basis

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In this linear algebra lecture, I am going to discuss extending and shrinking a set to form a basis. In particular, I will talk about removing vectors from a spanning set to form a basis for the vector space. Moreover, I will also discuss how to extend a linearly independent set to a basis.

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⏰ Timestamps
0:00 Introduction
0:04 Turning a spanning set of a vector space to a basis
1:45 Example 1: Using inspection
4:53 Example 1: Using row echelon form
7:27 Example 2: Shrinking a spanning set of P^3 to a basis
10:11 Example 3: Find the dimension of the following subspace of R^3
14:11 Extending a linearly independent set to a basis
15:34 Steps to extend a linearly independent set to a basis
16:00 Example of extending a linearly independent set to a basis

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