$$59 \mathbf{A} = \mathbf{A}^{-1}, \mathbf{B}^{-1} = \begin{bmatrix} 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \end{bmatrix}$$

$$(\mathbf{AB})^{-1} = \begin{bmatrix} 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 \ 0 & 0 & 1 & 0 \ 0 & 1 & 0 & 0 \end{bmatrix}$$

$$60 \text{ (a) } \begin{bmatrix} 1 \ 2 \end{bmatrix} \quad \text{(b) } \begin{bmatrix} 1 \ -4 \ 0 \end{bmatrix} \quad \text{(c) } \begin{bmatrix} -1 \ 2 \end{bmatrix} \quad \text{(d) } \begin{bmatrix} 4 \ 3 \ 2 \ 1 \end{bmatrix}$$

$$61 \begin{bmatrix} \cos(-\frac{\pi}{8}) \ -\sin(-\frac{\pi}{8}) \end{bmatrix}$$

$$62 \begin{bmatrix} -j \ 1 \ j \end{bmatrix}$$

$$63 \frac{1}{12} \begin{bmatrix} -7 & -6 & 5 \ 2 & 0 & 2 \ 1 & -6 & 1 \end{bmatrix}$$

$$x = 2, y = 1, z = 2$$

$$64 \quad \alpha = 1 \quad x = \lambda \quad y = 5\lambda \quad z = 7\lambda$$

$$\alpha = -6 \quad x = \mu \quad y = -2\mu \quad z = 0$$

$$65 -6, -3, -2$$

$$66 \text{ (a) } a = 0 \quad \text{(b) } \frac{1}{9} \begin{bmatrix} 1 \ 7 \ 6 \end{bmatrix} \quad \text{(c) } \begin{bmatrix} \lambda \ \lambda \ \lambda \end{bmatrix} \quad \text{(d) } \begin{bmatrix} -2 \ 1 \ 3 \end{bmatrix}$$

$$67 \begin{bmatrix} 0.1896 & -0.0604 & -0.0167 & 0.0167 & -0.0021 & -0.0021 \ -0.0604 & 0.2088 & -0.0551 & -0.0218 & 0.0171 & -0.0021 \ -0.0167 & -0.0551 & 0.2103 & -0.0564 & -0.0218 & 0.0167 \ 0.0167 & -0.0218 & -0.0564 & 0.2103 & -0.0551 & -0.0167 \ -0.0021 & 0.0171 & -0.0218 & -0.0551 & 0.2088 & -0.0604 \ -0.0021 & -0.0021 & 0.0167 & -0.0167 & -0.0604 & 0.1896 \end{bmatrix}$$

$$\begin{bmatrix} 0.1875 \ -0.0625 \ 0 \ 0 \ -0.0625 \ 0.1875 \end{bmatrix}$$

$$68 \quad a = u_1 \quad b = (-u_1 + u_2)/p \quad c = (-u_1 + u_3)/q$$

$$d = (u_1 - u_2 - u_3 + u_4)/pq$$

$$69 \quad x = 0.5889u \quad y = 0.4222u \quad z = 0.2222u$$

$$70 \quad a = -0.4011 \quad b = 1 \quad c = -0.5825$$

$$f(1) = 1.4345$$

$$71 \quad y_1 = 1.8936 \quad y_2 = 4.6809 \quad y_3 = 8.1489 \quad y_4 = 10.7660$$

$$72 \text{ (a) } \begin{bmatrix} -3 \ 0 \ 2 \end{bmatrix} \quad \text{(b) } \begin{bmatrix} -3 \ 2 \ 4 \end{bmatrix} \quad \text{(c) } \begin{bmatrix} -\frac{3}{25} \ \frac{1}{150} \ \frac{2}{75} \end{bmatrix}$$

$$73 \quad x = 1 \quad y = 2 \quad z = 2 \quad t = 3$$

$$74 \quad x = -0.0833 \quad y = 0.7083 \quad z = 1.9167 \quad t = 2.9583$$

$$75 \text{ (a) } \begin{bmatrix} 1.1602 \ -0.0515 \ 0.0065 \end{bmatrix} \quad \text{(b) } \begin{bmatrix} 2.6844 \ 0.0234 \ 2.3569 \end{bmatrix} \quad \text{(c) } \begin{bmatrix} -1.3424 \ 1.2860 \ 2.4458 \ 0.5511 \end{bmatrix}$$

$$76 \begin{bmatrix} -74.17 \ -25.54 \ 140.11 \end{bmatrix}, \det = 0.002725 \begin{bmatrix} -142.53 \ -50.52 \ 262.77 \end{bmatrix}, \det = 0.001453$$

$$78 \quad 4.5, 8, 10.5, 12, 12.5$$

$$79 \text{ Solution: } 1, 2, 2, 3$$

$$\text{After 5 iterations: } 0.989, 1.99, 1.98, 3.00$$

$$80 \text{ Solution: } -0.083, 0.708, 1.917, 2.958$$

$$\text{After 3 iterations: } -0.189, 0.634, 1.868, 2.920$$

$$81 \text{ (a) } 0.8 \quad \text{(b) } 1.1 \quad \text{(c) } \text{no convergence}$$

$$82 \begin{bmatrix} 10 \ 20 \ -30 \end{bmatrix}$$

在……中不存在收敛 50 iterations, 甚至从一个

$$\text{starting value of } \begin{bmatrix} 10.1 \ 19.9 \ -29.9 \end{bmatrix}$$

$$83 \quad I_1 = 0.5172, I_2 = 0.4914, I_3 = 0.8017$$

$$84 \quad 0.1685, 0.3258, 0.5282, 0.7188, 0.9563, 1.0063,$$

$$0.8063, 0.6064, 0.4059, 0.2079$$

$$85 \text{ (a) } 2, 2, [2/3, -1/3] \quad \text{(b) } 1, 2, \text{ inconsistent}$$

$$\text{(c) } 2, 2, [1, -t, t] \quad \text{(d) } 2, 2, [2 - t, 1, t]$$

$$\text{(e) } 2, 3, \text{ inconsistent} \quad \text{(f) } 4, 4, [0, 1/3, 0, 1]$$