행렬 $\begin{pmatrix*}[r] 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 \end{pmatrix*}$ 의 최소다항식(minimal polynomial)은?

• ①$x ^ {2} -3x+2$
• ②$x ^ {3} -4x ^ {2} +5x-2$
• ③$x ^ {3} -5x ^ {2} +8x-4$
• ④$x ^ {4} -5x ^ {3} +9x ^ {2} -7x+2$
• ⑤$x ^ {4} -6x ^ {3} +13x ^ {2} -12x+4$