Find The Eigenvectors and Eigenvalues

Purpose: To see what an eigenvector is in two dimensions The vector [b]u[/b] is being multiplied by the matrix: A = {{15/7,-4/7},{2/7,6/7}} The resulting vector is shown in red. Change the vector [b]u[/b] by dragging its tip to a different location.

[b]1.[/b] Find two different vectors in quadrant I whose directions are unaffected by multiplication by the matrix [i]A[/i]. These vectors are called [i]eigenvectors[/i] for the matrix [i]A[/i]. [b]2.[/b] Notice that a vector pointed in the opposite direction of an eigenvector is still an eigenvector. [b]3.[/b] If multiplying an eigenvector by its matrix changes its length by a certain factor, then this factor is called an [i]eigenvalue[/i] for that eigenvector. Find the eigenvalues for each of the eigenvectors you found in problem 1. [Note: An eigenvalue can be any number... positive, negative or zero]