Eigenvalues of a 3x3 matrix  Alternate coordinate systems (bases)  Linear Algebra  Khan Academy  Summary and Q&A
TL;DR
This video explains how to find the eigenvalues of a 3x3 matrix by using the determinant of lambda times the identity matrix minus A.
Questions & Answers
Q: What is the definition of an eigenvalue?
An eigenvalue is a scalar lambda that satisfies the equation A * v = lambda * v, where A is a matrix and v is a nonzero vector.
Q: How can eigenvalues be found for a 3x3 matrix?
Eigenvalues can be found by solving the characteristic equation, which is the determinant of lambda times the identity matrix minus A equal to zero.
Q: Why is it important to find the eigenvalues of a matrix?
Eigenvalues provide important information about a matrix, such as its determinant, trace, and eigenvectors, which can be used to solve systems of linear equations and analyze linear transformations.
Q: How are the possible eigenvalues determined?
The possible eigenvalues are the values of lambda that make the determinant of lambda times the identity matrix minus A equal to zero.
Summary & Key Takeaways

Eigenvalues for a 3x3 matrix can be found by determining if the determinant of lambda times the identity matrix minus A is equal to zero.

The characteristic polynomial for a 3x3 matrix is lambda  3 * (lambda + 3) * (lambda  3) = 0.

The possible eigenvalues for the 3x3 matrix are lambda = 3 and lambda = 3.