The top matrix on the menu is the diagonal matrix

Initially, when you select this matrix, the vectors x and Ax should both be aligned along the positive x axis. What information about an eigenvalue-eigenvector pair is apparent from the initial figure positions? Explain. Rotate x counterclockwise until x and Ax are parallel, that is, until they both lie along the same line through the origin. What can you conclude about the second eigenvalue-eigenvector pair? Repeat this experiment with the second matrix. How can you determine the eigenvalues and eigenvalues of a 2 × 2 diagonal matrix by inspection without doing any computations? Does this also work for 3 × 3 diagonal matrices? Explain.

Transcribed Image Text:

A =