See the attached file.
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
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Eigenvectors from transformations (reflection, shear and rotation) are investigated. The solution is detailed and well presented.