20．矩陣M=$[\begin{array}{l}{3}&{6}\\{5}&{2}\end{array}]$有屬于特征值λ₁=8的一個(gè)特征向量e₁=$[\begin{array}{l}{6}\\{5}\end{array}]$，及屬于特征值λ₂=-3的一個(gè)特征向量e₂=$[\begin{array}{l}{1}\\{-1}\end{array}]$．
（1）對(duì)于向量$\overrightarrow{α}=[\begin{array}{l}{3}\\{8}\end{array}]$，記做$\overrightarrow{α}={e}_{1}-3{e}_{2}$，利用這一表達(dá)式計(jì)算${M}^{3}\overrightarrow{α}$，${M}^{50}\overrightarrow{α}$；
（2）對(duì)于向量$\overrightarrow{β}=[\begin{array}{l}{8}\\{3}\end{array}]$，計(jì)算 ${M}^{5}\overrightarrow{β}$，${M}^{100}\overrightarrow{β}$．