Exercise 10

Suppose that $W$ is a plane in $\real^3$ and that $P$ is the $3\times3$ matrix that projects vectors orthogonally onto $W$.

1. Explain why $P$ is orthogonally diagonalizable.

2. What are the eigenvalues of $P$?

3. Explain the relationship between the eigenvectors of $P$ and the plane $W$.