Suppose and .
If possible, complete the following equations; otherwise, enter DNE.
The linear transformation acts like multiplication by
in the subspace .
Is the vector an eigenvector for ?
choose
yes
no
cannot be determined
If so, what is its associated eigenvalue?
Is the vector an eigenvector for ?
choose
yes
no
cannot be determined
If so, what is its associated eigenvalue?
Are the vectors and in the same eigenspace?
choose
yes
no
cannot be determined
If the vector is an eigenvector for with eigenvalue , then
The linear transformation acts like multiplication by in the subspace
. Enter your answer as a coordinate vector of the form <1,2>.
Is the vector an eigenvector for ?
choose
yes
no
cannot be determined
If so, what is its associated eigenvalue?
You can earn partial credit on this problem.