Finding Eigenvalues and Eigenvectors

The video tutorial introduces eigenvalues and eigenvectors, explaining their significance in linear algebra and applications in physics. It provides a step-by-step guide to solving for eigenvalues and eigenvectors using matrix operations, including examples with 2x2 and 3x3 matrices. The tutorial concludes with an advanced example to reinforce understanding.

Can a matrix have more eigenvalues than its dimensions? Explain your answer.

What is the characteristic polynomial and how is it related to eigenvalues?

Discuss the role of row operations in finding eigenvectors.

Provide an example of how to find an eigenvector for a given eigenvalue.