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How to Find Eigenvalues and Eigenvectors of a 3x3 Matrix

Learn how to find the eigenvalues and eigenvectors of a 3x3 matrix step by step! This video walks through solving det(A - λI) = 0 to find the eigenvalues and then finding a basis for each eigenspace. You'll also see the geometric interpretation of the eigenspaces in R³. Perfect for students studying linear algebra and looking for clear examples. What You’ll Learn: • How to compute eigenvalues of a 3x3 matrix • How to find the eigenspaces for each eigenvalue • How to interpret eigenspaces geometrically Linear Algebra Playlist    • Linear Algebra Full Course: Step-by-S...   Eigenvalues and Eigenvectors    • Mastering Eigenvectors and  Eigenvalu...      • How to Find Eigenvalues and Eigenvect...      • Eigenvalues and The Characteristic Eq...      • Diagonalizing Matrices: Eigenvalues, ...      • Understanding Population Dynamics wit...   Subscribe to My YouTube Channel    / @understandthemath   Visit the Understand The Math Website https://www.understandthemath.com Find free guided notes, filled in guided notes for purchase, course outlines/playlists, and math merchandise. Connect on Social Media Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Pinterest: https://pin.it/2YAWfM2zP 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. #linearalgebra #eigenvalues #eigenvectors #matrices #mathhelp #mathstudent #studyguide #engineeringmath #collegealgebra #matrixmath #learnmath