This applet aims to help visualize the geometrical interpretation of the eigenvector(s) and eigenvalue(s) of a 2-by-2 matrix.[br][br]In this applet, users may[br]- define the 2-by-2 matrix by entering the values of the elements,[br]- drag the point V to view the vector [b]v[/b] and the vector [i]Av[/i] in the same diagram,[br]- receive a notification when an eigenvalue that satisfies [i]Av=kv[/i] is found.

1. What are the eigenvectors and the corresponding eigenvalues of [math]{{2,3},{4,1}}[/math]?[br]2. How many eigenvalues can a 2-by-2 matrix possibly have?[br]3. How many eigenvectors can a 2-by-2 matrix possibly have?[br]4. What can you say about the eigenvector(s) and eigenvalue(s) of a 2-by-2 matrix whose determinant is 0?