# Find The Eigenvectors and Eigenvalues

- Author:
- Nick Chura

Purpose: To see what an eigenvector is in two dimensions
The vector

**u**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**u**by dragging its tip to a different location.**1.**Find two different vectors in quadrant I whose directions are unaffected by multiplication by the matrix

*A*. These vectors are called

*eigenvectors*for the matrix

*A*.

**2.**Notice that a vector pointed in the opposite direction of an eigenvector is still an eigenvector.

**3.**If multiplying an eigenvector by its matrix changes its length by a certain factor, then this factor is called an

*eigenvalue*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]