What are the eigenvalues of ? List in order from smallest to largest. ,
What are the eigenvalues of ?

List in order from smallest to largest. ,

What are the eigenvalues of ?

List in order from smallest to largest. , ,

Is an eigenvalue of ?
Yes No
The eigenvalues of the echelon form of are not necessarily the same as the eigenvalues of . So row reducing to a triangular matrix and looking at the diagonal is not a valid method here. Instead consider the equation .

Which of the following is an eigenvector of ?
A nonzero vector is an eigenvector of if is a multiple of , in other words if for some .

True/False: To find the eigenvalues of are the entries in the main diagonal of where is an echelon form of .
True False
Question 4 is a counter example.

True/False: The scalar zero is an eigenvalue of if and only if is not invertible.
True False
Zero is an eigenvalue of means has a nontrivial () solution. Use the IMT.