By geometric reasoning, find eigenbases for the following linear transformations. For each

eigenvector in your eigenbasis, also specify its eigenvalue.

a. Orthogonal projection onto the planex+ 2y+ 3z= 0.

b.Reflection across the planex+ 2y+ 3z= 0.

c. 180 degree rotation around a line perpendicular to the planex+ 2y+ 3z= 0.

Then use your answers to find 33 matrices which accomplish the above transformations.