设 [tex=7.929x1.357]YsxUk3RpCEL54ROD5kt0RG4RdYBHWdoxANQx3JTdac77uLGuBPTqCX1UVkx/nwrdL+JOqOSkvzlOFW/Z2cSd0y+OchVdXtLgfWh46aTzGtaVlbT516VttYLLvOsiewVzTTyoO1QKVoBOnyhNUm+OCg==[/tex]，[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex] 可逆对称，[tex=2.714x1.143]hT+oJ7OUfFv/vJSX4KjeNUUvGM5B05U/r8XjBAy3eD+jezKNYk6LbiOz3UjY1dAc[/tex]，证明存在可逆方阵 [tex=0.857x1.0]qe7VJd3WNwd2RMskb5AGFuRGpE3QsV7ZzZ9bL+uB/1s=[/tex]，使 [tex=7.5x2.786]vh3bmbpS/BR/vgs0iDMC5RU+5s8Q81GSlSX/+lT2KIEWhiPMNOJkYK/k6uGb1a3Q9RKQTNDEulqlHU7o/ngiVYBcdreUZR0bkBwmt/cO626shh4YU6PQd/15616//Wcq/kkg58cFZMrMirl7+BVTw8PVk74bs0C4dOGB/E68JTA/YFggRSgK4g92VKWm2tRgItQJMW+TKkm4PoOgIfvQTA==[/tex] 为准对角矩阵.

2022-05-29

设 [tex=7.929x1.357]YsxUk3RpCEL54ROD5kt0RG4RdYBHWdoxANQx3JTdac77uLGuBPTqCX1UVkx/nwrdL+JOqOSkvzlOFW/Z2cSd0y+OchVdXtLgfWh46aTzGtaVlbT516VttYLLvOsiewVzTTyoO1QKVoBOnyhNUm+OCg==[/tex]，[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex] 可逆对称，[tex=2.714x1.143]hT+oJ7OUfFv/vJSX4KjeNUUvGM5B05U/r8XjBAy3eD+jezKNYk6LbiOz3UjY1dAc[/tex]，证明存在可逆方阵 [tex=0.857x1.0]qe7VJd3WNwd2RMskb5AGFuRGpE3QsV7ZzZ9bL+uB/1s=[/tex]，使 [tex=7.5x2.786]vh3bmbpS/BR/vgs0iDMC5RU+5s8Q81GSlSX/+lT2KIEWhiPMNOJkYK/k6uGb1a3Q9RKQTNDEulqlHU7o/ngiVYBcdreUZR0bkBwmt/cO626shh4YU6PQd/15616//Wcq/kkg58cFZMrMirl7+BVTw8PVk74bs0C4dOGB/E68JTA/YFggRSgK4g92VKWm2tRgItQJMW+TKkm4PoOgIfvQTA==[/tex] 为准对角矩阵.

答案：

证  因为 [tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex] 可逆、对称，于是 [tex=1.857x1.214]c5Cf4pRARaBipYntugL/3ie5OUTtMdsQ6cWRbbnRY8c=[/tex] 对称. 注意到[tex=23.071x3.357]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[/tex][tex=30.929x3.357]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[/tex]，因此结论成立.

举一反三

内容

0
以下程序段实现的输出是（）。for(i=0;i<;=9;i++)s[i]=i;for(i=9;i>;=0;i--)printf("%2d",s[i]);[/i][/i] A: 9 7 5 3 1 B: 1 3 5 7 9 C: 9 8 7 6 5 4 3 2 1 0 D: 0 1 2 3 4 5 6 7 8 9
1
设DES加密算法中的一个S盒为： 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 15 12 8 2 4 9 1 7 5 11 A: 1010 B: 0001 C: 1011 D: 0111
2
输出九九乘法表。 1*1=1 2*1=2 2*2=4 3*1=3 3*2=6 3*3=9 4*1=4 4*2=8 4*3=12 4*4=16 5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 6*1=6 6*2=12 6*3=18 6*4=24 6*5=30 6*6=36 7*1=7 7*2=14 7*3=21 7*4=28 7*5=35 7*6=42 7*7=49 8*1=8 8*2=16 8*3=24 8*4=32 8*5=40 8*6=48 8*7=56 8*8=64 9*1=9
3
【单选题】Which of the following matrices does not have the same determinant of matrix B: [1, 3, 0, 2; -2, -5, 7, 4; 3, 5, 2, 1; -1, 0, -9,-5] A. [1, 3, 0, 2; -2, -5, 7, 4; 0, 0, 0, 0; -1, 0, -9, -5] B. [1, 3, 0, 2; -2, -5, 7, 4; 1, 0, 9, 5; -1, 0, -9, -5] C. [1, 3, 0, 2; -2, -5, 7, 4; 3, 5, 2, 1; -3, -5, -2, -1] D. [1, 3, 0, 2; -2, -5, 7, 4; 0, 0, 0, 1; -1, 0, -9, -5]
4
写一个文法G,使其语言为不以0开头的偶数集。 A: G[S]:S→AB|BA→AD|CB→2|4|6|8｜0C→1|3|5||7|9|B B: G[S]:S→AB|BA→AD|CB→1|2|3|4|5|6|7|8|9C→2|4|6|8｜0 C: G[S]:S→AB|BA→AD|CB→2|4|6|8｜0C→1|2|3|4|5|6|7|8|9D→0|C D: G[S]:S→AB|BA→AD|DB→2|4|6|8｜0D→1|2|3|4|5|6|7|8|9|0