The eigenvalues are in your given matrix.
Hey, I'm really struggling today.
We just started doing eigenvectors, and I'm supposed to solve this following problem without using determinants.
Prove that the eigenvectors of the matrix
generate a 2-Dimensional space and give a basis for it. Also, state the eigenvalues. I just don't think this stuff is harder than some of the other stuff I've done, but I'm really pathetic right now.