Consider the matrix A=(010001−c−b−a)A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -c & -b & -a \end{pmatrix}A=00−c10−b01−a. What is det(A−λI)\det(A - \lambda I)det(A−λI)?
−(λ3+aλ2+bλ+c)-(\lambda^3 + a\lambda^2 + b\lambda + c)−(λ3+aλ2+bλ+c)
λ3+aλ2+bλ+c\lambda^3 + a\lambda^2 + b\lambda + cλ3+aλ2+bλ+c
−(λ3−aλ2+bλ−c)-(\lambda^3 - a\lambda^2 + b\lambda - c)−(λ3−aλ2+bλ−c)
λ3−aλ2+bλ−c\lambda^3 - a\lambda^2 + b\lambda - cλ3−aλ2+bλ−c