Question: 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

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.

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