若[tex=3.071x1.214]wQ/cVPtUw1FrqD5sLlaQDQ==[/tex]是线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的两个子空间，证明：[tex=22.571x1.357]lBXXZYMMrxJ2+/5vAU9EvSU84vThpvGfkTUbMdjmmggoyhJmUGzn3O7DMlDBRwDaMsviT88rNr84r97OiDMYgxSGlKY3QgVcm1WHvXGRvefdZmmvTjeXqfEFs3Xbm0uvVjyhQ+jgIquh0iPdTZx4VcbjTl73iOv9r2mAj7U7QeVhN9Z4NmFOyiGKsIdi8JL6[/tex]，这里[tex=2.714x1.0]3pUWlQ1tmh/N4ENzskpzEg==[/tex]表示子空间[tex=1.0x1.0]0e+76hgEqXhGRszRQWFSzQ==[/tex]的维数．
设[tex=3.071x1.214]aKCzKguPwZrqT3KIz/rPig==[/tex]的维数分别为[tex=6.5x1.214]68Y5thPYen0jO9RlgighAO2BxtYauqs/8LLU/iurA6rVtS7VTns354En5ce+WwJy[/tex]的维数为[tex=0.5x0.786]Tg0I1PUwmDJ7uXa9+yiYMA==[/tex]，取[tex=3.714x1.214]+cHBqSg7Z0OPsp8jR9MmJm+3ROoxuBSoFdo3LyOiMz0=[/tex]的一组基[tex=1.286x1.357]joCnEPxmqDbCpKU1ycYYgQ==[/tex][tex=4.429x1.0]F/LyQ52SJ4CGXCgTf9A8Uvl4GnJwr68LsH9hMwyO6PzB5bqA0b/v2Y9paviZAHxH[/tex]，并将[tex=1.286x1.357]joCnEPxmqDbCpKU1ycYYgQ==[/tex]扩大为[tex=1.357x1.214]m3mI6l/jT9E/N9Rn6p+KkQ==[/tex]的一组基[tex=1.714x1.357]+H3Xid4Jl25CmyvfHhg7lg==[/tex][tex=10.0x1.429]A4bb/tPHkJ9j+Isn2S8dabTbO+D5fftiMhGYxnRNDBldkBfzzC8wO3CZNTns3pIy1lqJzMagCy0NmKXDdaIUV+PpgSltj1oqnDgpVllAU8A=[/tex]再将[tex=1.286x1.357]joCnEPxmqDbCpKU1ycYYgQ==[/tex]扩大为[tex=1.357x1.214]hs0OB4TQKckEpJIqmxLiaw==[/tex]的一组基[tex=2.143x1.357]niso8+c4tMOLmg3o+K1HrQ==[/tex][tex=9.786x1.286]A4bb/tPHkJ9j+Isn2S8daXYH6p7JZT5BZIUGQbMfMuS3Po+29nbkOxrKVeeBoXu3cLP+eM1ajBIPWkxlAIA316HIdmIm7gWVBdWU7ARJQZA=[/tex]令[tex=1.857x1.357]Xe1RmI1ec1omKMPVtL4eaw==[/tex]为[tex=15.429x1.286]xYCl2OMDQWXFQ6S8q11znswYOzles8dRDDOhmEIy3XJ7c9uqH9Sx1ukf+Y8M40lTMPxz9Hdk2NnwPSeyJswj6jyIkbo6xc4S+1hF7xSasruGJCvhnYCPpW+abcUpfePcMk7FQXeJNTxYTChYxm6XJU0Ie6Y0SREUjqU2JQStsRo=[/tex]，则[tex=18.571x1.357]P9ppD+Y9xWUxGzI/pyE0S3TzHHTjQ5LM9MYHEzG0bcq8OPED2BHu1v1f8olpiSubeONqessF/BsN83DbijvjiXWv3lnMw86RUgljK1z9n/SKavyHfVuNmB4/GIwmt28kp/SbPa8BAvHFz6pMmYDyPA==[/tex](1)[tex=19.214x1.357]xWOYizFH4W5Y8M5JTdP5YXAc29nqVhidpH3TWGiIL4DCQlnkToIYJWg6jw8urExPTZZx9uhjMYLl2wcJioedFodpReXhfR+f0c4jfA1VcNl8ilZy5txFANUyXDNymjwZh8sjT6II14cOUwI1vwx/d0htF/Ouatb/IsHd+Lek7Gk=[/tex]（2）[tex=19.0x1.357]XfLwfG/IIYuAFGch+BgA8wpiagjWL+JnF8CFrnfw39I6k89LsAR2jt63F/jBHSgjlU3FpwMmgbeE7Q4b8uqIAKHD3W4K+ZmUZ7DDmdSM0THc8rTs8uXlvebIkZLi4loqgMKKk+R/ni8Wy6Bq+NIpB/t7eeaLegeMpgBbB5du/lg=[/tex](3)易证[tex=21.857x1.357]hhY2ZL5RaFtbCy13i/HHmBFn55R84cGpdaE7CLeD8qcjouRVjrUBSmjUudvcVz4tQmPXy9hiVCQ3S13t/tbT5Fzf52t0cJ2s2ZjN3aY9GwhWpxvIYGP4z4612pjNFrst5SAc98NdrSUAUMkD4M1scXw/zp5wGYhg4afh8vUKFIo+vRWa0xyHVZRVOkRwsNL0[/tex]（4）下面证明[tex=15.643x1.286]OuL7ErdMElt/FGtNEk1RaHPAAVFRRDC3guwSiNL5PmDjODsZ2IGaVdsOOIjCQXYUzrQjIsBmheoJvikjrW5HkvoLmr/EIQ4+VCIuQRS9ITLSrOmHOZgkhggQmAlSnJG0Y14RiSLo1x44JPAL/aGlwQ==[/tex]线性无关．设[tex=28.929x1.286]TinSXfPNqsSTGDd3/k6bfXoFjpLPtK6W5sBkVlQ/geKv4535nOk6iWETseOFprXslQPtQHgAQyn/gWb0qIX4oPSYKiFMvnsARVPwRlgAsFGEwu6d51q4ByyCrtdnu9o8MMff+fX7Rpl1bCnZDGc/ikfdiON/CS1twYIYdUfoC/+2VH7eCHOvzg2I89ZvdLKirOyr/Cxn0FDeu6u4w5oY1A==[/tex](5)令[tex=18.429x1.286]JFvJVtoMoWUlItP/bYTnIWeGeuLphHrp5+1oHJ0bynr84+Cx8yT16cWj2Rc09z9YwQOAUtDNq6Jj+IZ16eiefinn+qKIpBOAjXTBmrBaD6Uc3u5HwpXmr2/f4VyWPJ7AeHDexxjVIOvuD/Z96N+dnA==[/tex]（6）由(5)式有[tex=12.429x1.357]uftOqL+wKrPkl7uCyhXt1he/re3/UwzSoM1Vadz2d0CVtYIat22OLX5F9DcAQq/GpQ2s38oQnu3hHb3Lgzy7/1fJIuSh/YP7xoiy3PEluaA=[/tex](7)由(6)、(7)两式知[tex=6.571x1.214]xvSsQ8CPG38qnwFyEvlLDyQ7tTRG1Ln/0ZOdccrSMvQIjDPbjBjok8RyJrO8AD3Q[/tex]，从而[tex=5.5x1.214]xvSsQ8CPG38qnwFyEvlLD0cRNE/DSKbLeAPt1IV7EZw=[/tex]，所以[tex=8.571x1.143]UN88TFb9Vh/Qr8Fwshgd2ildB6NxnJhtKT7zQxxwEHGm54VE2M/xHHL9Dbq/3T0HAFsSJWI5SHEO7Hx3wRwW7A==[/tex]（8）由(8)带入(7)，并移项得[tex=19.214x1.286]LaJCiC/tn3WAmUBu1BWJic36bPj9U92PJSnE1jl4y15uwV9wdoA0MF+N2mnrM+VZn9FIw9711ZF+PDjy3b/nolD9+HWkodbobNjp4+cImFdrkIXUD5H7Md4uq22r3/qz8p7fjK9EHUTxn8jXj1mv9Q==[/tex]（9）但注意到[tex=10.0x1.286]xYCl2OMDQWXFQ6S8q11znv7z5x0U1Bi6G0lQzIYGFuDWlTj7XV1JC8GaChWjVh23ylGg8sDCWVuQ2C664JV1QcicYOC3yXp1KeaCZT0dZHk=[/tex]线性无关，由（9）式可得[tex=12.929x1.286]kM2wtE6z3Nxi2fz8l/wLEAz79U4cESBMf6shcencGies8xmZ6QymYgB/ZYfvRQ7I[/tex]（10）将(10)带入(8)得[tex=1.857x1.214]h5VGJOXOpmo66K8EKTGljA==[/tex].再带入(6)有[tex=18.857x1.286]HK8wYizuPgd9GrmWws4FsGqH8Qn4297n1Wgg2u4y56jAQCnGG0Ixw+QpHdfqVnA6Fj5TWyUw12oD6u8saIJ7Re84xyF6HeBbPU8zBvGMBYQaMg0tcqicaIaNW4lwreJmiZL1ss2a3uEaLJU5eFZt3A==[/tex]由[tex=10.0x1.286]OuL7ErdMElt/FGtNEk1RaHPAAVFRRDC3guwSiNL5PmDjODsZ2IGaVdsOOIjCQXYUe0/Jzk6ai21FmHL/la7FEA==[/tex]线性无关，可得[tex=15.0x1.286]sjK3QdwfJDuBFLJYGtKnpe7oEqrGTT/9BwPmgA7bEs1P7gY0o4VxUfPFPu6S6GsLkfaKhXBWtpP95R9O1Rac5A==[/tex](11)再由(10),(11)知[tex=15.571x1.286]OuL7ErdMElt/FGtNEk1RaHPAAVFRRDC3guwSiNL5PmDjODsZ2IGaVdsOOIjCQXYUY8UZJK8wwzCP0NvtUG0G3WLaxjLcpleNtwr/3VgcJ8+JwO9AQn+lJH2vPsSppgpsRFNUIxYN0cvDZCcR//M/Uw==[/tex]线性无关．再由（4）式知[tex=21.857x2.714]ObF0sBw1Gh1tpEYRkW5+c00ygZF0H9i3dNzk0TZ6ZmSI9ZWAjWAFuD5fbR5HJbwbVkCETruj5SeOcFLa/+vBkhwOtlru+n9e5CMUpox31hMIFmDkP0n253o+MgfKb7bnj3ZtcsUeb9gQNsXKB4K9u6ZRr753KdsuY2WsrmywiXg=[/tex]即[tex=22.571x1.357]lBXXZYMMrxJ2+/5vAU9EvSU84vThpvGfkTUbMdjmmggoyhJmUGzn3O7DMlDBRwDaMsviT88rNr84r97OiDMYgxSGlKY3QgVcm1WHvXGRvefdZmmvTjeXqfEFs3Xbm0uvVjyhQ+jgIquh0iPdTZx4VcbjTl73iOv9r2mAj7U7QeVhN9Z4NmFOyiGKsIdi8JL6[/tex]
举一反三
- >>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- 设[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]是有限维线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的线性变换，[tex=1.0x1.0]0e+76hgEqXhGRszRQWFSzQ==[/tex]是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的子空间，[tex=1.714x1.0]xIy1AT19mrzIEEo5ZeH+0A==[/tex]表示由[tex=1.0x1.0]0e+76hgEqXhGRszRQWFSzQ==[/tex]中向量的像组成的子空间，证明：[tex=18.0x1.571]lBXXZYMMrxJ2+/5vAU9EvUMjF2EjPNhXdhxshHJhWR5XKEUfpmEWqqipid115QO+Se1ZwcFo29oVwLnqDA4U/LY08VLkqkIskbWQTSVYUsK7yqTiCnOU9+rFk9A8bWyIReqN+vhVvIdX9yigoWZPqA==[/tex]
- 【计算题】5 ×8= 6×4= 7×7= 9×5= 2×3= 9 ×2= 8×9= 7×8= 5×5= 4×3= 5+8= 6 ×6= 3×7= 4×8= 9×3= 1 ×2= 9×9= 6×8= 8×0= 4×7=
- 6个顶点11条边的所有非同构的连通的简单非平面图有[tex=2.143x2.429]iP+B62/T05A6ZTM0eeaWiQ==[/tex]个，其中有[tex=2.143x2.429]ndZSw3zT0QTOVLVdoUto1Q==[/tex]个含子图[tex=1.786x1.286]J+vVZa2YaMpc6mJBbqVvWw==[/tex]，有[tex=2.143x2.429]lmhx48evnQMhi03NovPXig==[/tex]个含与[tex=1.214x1.214]kFXZ1uR8GjycbJx+Ts2kyQ==[/tex]同胚的子图。供选择的答案[tex=3.071x1.214]3KinXFh3SXhZ7nIe1y9KEV6aadxhhJWeEy6Dij1iObdMUZkY6ZA5J2dVVjPSuhEf[/tex]：(1) 1 ;(2) 2 ;(3) 3 ; (4) 4 ;(5) 5 ;(6) 6 ; (7) 7 ; (8) 8 。
内容
- 0
【单选题】请用地点定桩法在4分钟内记忆数字。 4 0 1 3 6 3 5 1 9 8 8 9 7 2 9 3 0 9 5 3 1 7 7 5 2 3 3 0 5 0 1 4 1 3 8 3 5 7 9 7 (5.0分) A. 已背 B. 未背
- 1
【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]
- 2
设[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]是域[tex=0.786x1.286]BlkXDnmzWHxe4M6E9LlofQ==[/tex]上的有限维线性空间，[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]上的一个线性变换，[tex=1.0x1.0]0e+76hgEqXhGRszRQWFSzQ==[/tex]是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一个子空间，用[tex=2.643x1.214]KdJTfdOLEBWMXQir5AfhBQ==[/tex]表示[tex=1.0x1.0]0e+76hgEqXhGRszRQWFSzQ==[/tex]在[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]下的原象集，证明：[tex=2.643x1.214]KdJTfdOLEBWMXQir5AfhBQ==[/tex]是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一个子空间，且[tex=15.571x1.571]lBXXZYMMrxJ2+/5vAU9EvVvBGnLtY5JG8CbyUBVipe1uKDCQ1/KMuX64J9SLCi3ar2m76lz6zTaMR/0PayL319rvQLU4zhEdMizyHv9JVIUABc0jzkHxvW8wRmhsuQQnu66lpQQHQ5Y6rNUSTKc/IJw3GVC2rz/DOYqBVzfdYTs77YU3Muuc0/toyWs+9rVf2Yiw28jepiPWOuG3qlOl0Q==[/tex]。
- 3
假设“☆”是一种新的运算，若3☆2=3×4，6☆3=6×7×8，x☆4=840(x＞0)，那么x等于： A: 2 B: 3 C: 4 D: 5 E: 6 F: 7 G: 8 H: 9
- 4
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