已知有向曲线 L 为球面 $x^{2} + y^{2} + z^{2} = 2x$ 与平面 $2x - z - 1 = 0$ 的交线从 $z$ 轴正向往 $z$ 轴负向看去为逆时针方向，计算曲线积分 $\int_{L}(6xyz - yz^{2})dx + 2x^{2}zdy + xyzdz$ 已知数列 $\{x_{n}\},\{y_{n}\},\{z_{n}\}$ 满足 $x_0 = -1, y_0 = 0, z_0 = 2$ 且 $\left\{ \begin{array}{l} x_n = -2x_{n-1} + 2z_{n-1} \\ y_n = -2y_{n-1} - 2z_{n-1} \\ z_n = -6x_{n-1} - 3y_{n-1} + 3z_{n-1} \end{array} \right.$ , 记 $\alpha_{n} = \left\{ \begin{array}{l}x_{n}\\ y_{n}\\ \vdots \end{array} \right\}$ ，写出满足 $\alpha_{n} = A\alpha_{n - 1}$ 的矩阵 $A$ ，并求 $A^n$ 及 $x_{n},y_{n},z_{n}(n = 1,2,\dots)$ 21. 22. 设总体 $X - U(0,\theta)$ ， $\theta$ 未知， $X_{1},X_{2}\dots X_{n}$ 为简单随机样本， $$ X _ {(n)} = \max \left(X _ {1}, X _ {2} \dots X _ {n}\right), T _ {c} = c X _ {(n)}. $$