<s>[INST] Finding the Standard Matrix of a Linear Transformation The question is asking for Find the characteristic polynomial of the matrix:
$$
A =  \begin{bmatrix}
        5 & 5 & 0 \\
        0 & 4 & -5 \\
        -1 & 3 & 0 \\
        \end{bmatrix}$$
Answer is suppose to be an equation where $p(x)= \ldots$?
I approached this by knowing that the The characteristic polynomial for $A$ is given by $|A - \lambda I|$
so $$A = \begin{bmatrix}
        5-x & 5 & 0 \\
        0 & 4-x & -5 \\
        -1 & 3 & 0-x \\
        \end{bmatrix}$$
I found the determinant through the first row and I did
\begin{align*}
(5-x) [-x(4-λ) + 15] - 5[0 - 5] &  = (5 - x) (x^2 - 4x + 15) + 25\\
& = -x^3 + 9x^2 - 35x + 100
\end{align*}
but webwork is telling me it's incorrect. 
 [/INST] It looks like your solution is correct.
</s>