Aim

The aim of this experiment is to determine the eigenvalues and eigenvectors of given matrices using computational techniques and to understand their significance in linear algebra and applications.

Specifically, the objectives are:

1. To represent a given system or transformation in matrix form.
2. To compute the eigenvalues of the matrix using appropriate numerical or analytical methods.
3. To calculate the corresponding eigenvectors for each eigenvalue.
4. To verify the eigenvalue–eigenvector relationship for the obtained results.
5. To interpret the meaning of eigenvalues and eigenvectors in terms of scaling and direction of linear transformations.
6. To recognize the importance of eigen-analysis in areas such as stability analysis, principal component analysis, vibration modes, and other engineering and scientific applications.