The Characteristic Polynomial

Introduction

Which of the following is the characteristic polynomial of $A = \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix}$?

What are the eigenvalues of the upper triangular matrix

In one word: the polynomial $\det(A - \lambda I)$ is called the ______ polynomial of $A$.

Find the eigenvalues of $A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$, entered in increasing order, separated by commas (for example: 1,2).

Find the eigenvalues of

entered in increasing order, separated by commas (for example: 1,2,3).

In your own words, state the single most important definition or theorem of this section, and explain what it says.