Mastering One-to-one And Onto Transformations | Simplifying Linear Algebra

In this video, we explore One-to-One and Onto transformations, key concepts in Linear Algebra. You'll learn how to determine if a linear transformation is One-to-One and/or Onto using matrix representations, pivots, and step-by-step examples. We’ll also discuss real-world applications of these transformations in fields such as cybersecurity, quantum mechanics, and molecular biology.

🔑 Key Topics:
What are One-to-One Transformations?
What are Onto Transformations?
How to find pivots in matrices to determine One-to-One and Onto transformations.
Real-world applications of these transformations.

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*Timestamps*
00:00 Introduction to One-to-One and Onto Transformations
00:32 Definition of One-to-One Transformations
01:35 Definition of Onto Transformations
02:48 Example 1: Determining One-to-One and Onto Transformations
05:30 Example 2: Solving for Pivots in a Square Matrix
07:02 Real-World Applications of One-to-One and Onto Transformations
09:00 Conclusion and Preview of Next Video on Matrix Multiplication

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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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