Something that worked for me...Eigenvectors via Excel.

Our students meet eigenvalues and eigenvectors in year 1 of their course. A couple of years ago, I wrote an EXCEL spreadsheet which enables them to find the eigenvalues and eigenvectors of a 2x2 matrix experimentally. The idea, at its simplest, is that the spreadsheet allows the student to supply a 2x2 matrix (A, say) and then to rotate a unit vector, u, about the origin, with the spreadsheet showing, at every stage, the vector u and the transformed vector Au. The student then merely rotates u until the original unit vector and the transformed vector Au point in the same direction. The components of vector u can then be read off from the spreadsheet, as can the magnitude of Au (which, since u is a unit vector, gives the magnitude of the eigenvalue)…The author presents a spreadsheet that has been used by students to help discover the eigenvalues and eigenvectors of a 2 x 2 matrix experimentally. Includes a link ref to the actual student worksheet and spreadsheet....