3 x 3 Eigenvalues and Eigenvectors

This video provides a complete step-by-step solution on how to find the eigenvalues and eigenvectors of a 3×3 matrix using the characteristic equation det(A − rI) = 0, determinant expansion, and systematic row operations. You will learn how to correctly form the identity matrix, compute eigenvalues, and then determine the corresponding eigenvectors through augmented matrices and row reduction techniques. The lesson carefully explains each stage, including factorization of the characteristic polynomial and solving for eigenvectors associated with r = 1, r = 2, and r = 3, making it ideal for Engineering Mathematics, Linear Algebra, University exams, and problem-solving practice. This tutorial is especially helpful for students who struggle with eigenvector calculations in 3×3 matrices, offering a clear, exam-focused approach suitable for beginners and advanced learners alike.
What You'll Learn:
How to find the characteristic equation
Solving for eigenvalues from a 3×3 matrix
Finding the corresponding eigenvectors
Tips for simplifying calculations

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How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
   • 3 x 3 Eigenvalues and Eigenvectors  
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (II)
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How to Find Eigenvalues and Eigenvectors for 2x2 Matrices (II)
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