The companion matrix of a monic polynomial p(t)=tn+cn−1tn−1+⋯+c1t+c0p(t) = t^n + c_{n-1}t^{n-1} + \cdots + c_1 t + c_0p(t)=tn+cn−1tn−1+⋯+c1t+c0 is: C=(00⋯0−c010⋯0−c101⋯0−c2⋮⋮⋱⋮⋮00⋯1−cn−1)C = \begin{pmatrix} 0 & 0 & \cdots & 0 & -c_0 \\ 1 & 0 & \cdots & 0 & -c_1 \\ 0 & 1 & \cdots & 0 & -c_2 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & \cdots & 1 & -c_{n-1} \end{pmatrix}C=010⋮0001⋮0⋯⋯⋯⋱⋯000⋮1−c0−c1−c2⋮−cn−1
For p(t)=t3−2t2+3t−1p(t) = t^3 - 2t^2 + 3t - 1p(t)=t3−2t2+3t−1, what is det(C)\det(C)det(C)?
−1-1−1
111
222
−2-2−2