Eigenvectors from Transformations : Reflection, Shear and Rotation

In each part find as many linearly independent eigenvectors as you can by inspection (by visualizing the effect of the transformation of R^2). For each of your eigenvectors, find the corresponding eigenvalue by inspection; then check your results by computing the eigenvalues and bases for the eigenspaces from the standard matrix for the transformation.
a) Reflection about the x-axis.
b) Reflection about the y-axis.
c) Reflection about y=x.
d) Shear in the x-direction with factor k.
e) Shear in the y-direction with factor k.
f) Rotation through the angle θ.

Attached file(s):

homework0014.pdf  View File