Master Properties of Determinants and Row Reduction to Echelon Form | See Examples

Learn how elementary row operations—such as replacement, interchange, and scaling—affect the value of determinants, how to calculate determinants using row reduction to echelon form, and how to combine this method with cofactor expansion for efficient problem-solving.

Key topics include:
The effect of row operations on determinants
Using row reduction to simplify determinant calculations
Important properties of determinants, like product rules and inverse relationships
Practical examples to illustrate these concepts
How to use determinants to assess matrix invertibility and linear independence

*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
00:26 Elementary Row Operations and Determinants
05:19 Determinants by Row Reduction to Echelon Form
10:33 Properties of Determinants
15:44 Determinants to Determine Invertibility and Independence

*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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