Chapter 7.1, Problem 22E

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable. 22. The linear transformation with $T(\stackrel{\to }{\upsilon })=\stackrel{\to }{\upsilon }$ and $T(\stackrel{\to }{\omega })=\stackrel{\to }{\upsilon }+\stackrel{\to }{\omega }$ for the vectors $\stackrel{\to }{\upsilon }$ and $\stackrel{\to }{\omega }$ in ${ℝ}^2$ sketched below