The top matrix on the menu is the diagonal matrix A = 5 4 0 0 3 4 Initially, when you
Chapter 6, Problem 1(choose chapter or problem)
The top matrix on the menu is the diagonal matrix A = 5 4 0 0 3 4 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 eigenvectors of a 2 2 diagonal matrix by inspection without doing any computations? Does this also work for 3 3 diagonal matrices? Explain.
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