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 ?

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 .

Question 4 is a counter example.

True/False: The scalar zero is an eigenvalue of if and only if is not invertible.

Zero is an eigenvalue of means has a nontrivial () solution. Use the IMT.