##### Exercise3

Determine whether the following statements are true or false and provide a justification for your response.

1. The eigenvalues of a matrix $$A$$ are the entries on the diagonal of $$A\text{.}$$

2. If $$\lambda$$ is an eigenvalue of multiplicity $$1\text{,}$$ then $$E_\lambda$$ is one-dimensional.

3. If a matrix $$A$$ is invertible, then $$\lambda=0$$ cannot be an eigenvalue.

4. If $$A$$ is a $$13\times 13$$ matrix, the charasteristic polynomial has degree less than $$13\text{.}$$

5. The eigenspace $$E_\lambda$$ of $$A$$ is the same as the null space $$\nul(A-\lambda I)\text{.}$$

in-context