Determine if a Set is a Basis for a Vector Space: Step-by-Step Guide

In this video, we'll walk you through the concept of a basis for a vector space, covering the definition of a basis, linear independence, and spanning the space. We'll demonstrate how to test if a set of vectors forms a basis using examples in R^2 and R^3. You'll also learn how to use echelon form and determinants to determine if a set is linearly independent and spans the space. Additionally, we'll cover standard bases for common spaces like R^2, R^3, M_22 an P_2.

If you're studying linear algebra or looking to refresh your understanding of vector spaces, this video is perfect for you!

*Link to Guided Notes*
Free downloadable pdf of guided notes that will help you follow along with the video and use later to review what you learned.

_Linear Equations in Linear Algebra:_

_Matrix Algebra:_

_Determinants_

_Vector Spaces_

_Eigenvalues and Eigenvectors_

_Orthogonality and Least Squares_

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*Timestamps*
00:00 Introduction
00:27 Basis Definition
01:05 Checking for Linear Independence
02:57 Checking for Spanning
05:05 Standard Basis Examples
06:53 Examples of Determining if a Set is a Basis

*More About Understand The Math*
Understand The Math provides students and lifelong learners with access to free, straightforward, and engaging mathematics instruction. I’m Cheryl Hile, the founder of Understand The Math, and I’m passionate about ensuring that accurate and engaging mathematics instruction is available to everyone! I have a Ph.D. in Engineering Science and Applied Mathematics and have over 25 years of teaching experience at the university level. This channel provides videos that contain clear explanations, step-by-step problem solving strategies, and carefully worked out example problems. In the video descriptions, you'll find a link to free guided notes. Students can use these notes to highlight concepts and fill in answers to example problems while watching the videos, and later, they can review what they've learned.

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