Geometrically, the equation means that the vectors and lie on the same line. In the applet below, notice there are two vectors on the screen, the red vector is and the blue vector is . You can interact with the applet by clicking and dragging the red arrow around, which will result in the blue arrow moving (since changing causes to move as well). See if you can find eigenvectors corresponding to different matrices by dragging around , keeping in mind the geometric interpretation mentioned above. Can you also approximate the associated eigenvalues to each eigenvector, simply geometrically?