Think "geometrically". Draw a picture. Draw a vector v and the line in its direction. What does "project onto that line" mean for a general vector in your picture? You are told that A projects any vector onto v. What is Av?

If w is perpendicular to v, what is Aw?B. Any vector w perpendicular to v is an eigenvector for A corresponding to the eigenvalue lambda = −1.

A only has two eigenvalues and you found them in (A) and (B).C. lambda = 1 is an eigenvalue for A

Look at (A) again.D. The vector v is an eigenvector for A corresponding to the eigenvalue lambda = 1.

Look at (B) again.E. lambda = 0 is an eigenvalue for A

F. None of the above

I know how to find eigenvalues and eigenvectors, but I don't really know what they correspond to. It's so abstract, and I'm unsure of how to see this question.

Can anyone point me in the right direction?

Thanks.