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.