Given A=(010001−a−b−c)A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -a & -b & -c \end{pmatrix}A=00−a10−b01−c, what is the characteristic polynomial of AAA?
p(λ)=λ3+cλ2+bλ+ap(\lambda) = \lambda^3 + c\lambda^2 + b\lambda + ap(λ)=λ3+cλ2+bλ+a
p(λ)=λ3−cλ2−bλ−ap(\lambda) = \lambda^3 - c\lambda^2 - b\lambda - ap(λ)=λ3−cλ2−bλ−a
p(λ)=−λ3−cλ2−bλ−ap(\lambda) = -\lambda^3 - c\lambda^2 - b\lambda - ap(λ)=−λ3−cλ2−bλ−a
p(λ)=λ3+aλ2+bλ+cp(\lambda) = \lambda^3 + a\lambda^2 + b\lambda + cp(λ)=λ3+aλ2+bλ+c