设[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，证明：[tex=9.929x1.286]rPNN5zkDYQixR1Ja2BQQIhstF7f13xeA6IA93gEgehkTN6+GUqnaZ8Rqa0unpbXs[/tex]。

2022-11-02

设[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，证明：[tex=9.929x1.286]rPNN5zkDYQixR1Ja2BQQIhstF7f13xeA6IA93gEgehkTN6+GUqnaZ8Rqa0unpbXs[/tex]。

答案：

[b]证[/b] 设矩阵[tex=5.5x1.5]Rsl8HZic8qwgZs4teB9gj8gLrPDRxfKllz3Eg4P8yGyxV2SjpKWVefa9w6vBjdp7[/tex] 则[tex=5.857x1.357]gwUq0sF6Bu8rXs+QyRKpvobX/JVJ3tt5MJLFOiPUQAd4uBV61lMgrHpnjyCOUmSHJKmEEgAsRW8Wtyxqz+5+KQ==[/tex][tex=12.429x5.357]xN2RlmSr5dl2ScgdLbKsKSSGpancMV+8XBGA1deEHRa3hNlp4K0Qals5F6Hl8ThXxcgt//qDONpPEE/G8ZR0h+9ZltXPLBW8yFFrurzQcqqo7o5rQUKqFgFyKLJS4AeBLlf/5Sx8uYjko96DoDBQl5sE+OfgMROuCVI66Mz/h85kMggVl7S545FN5YhD615ysVrrqkHJPdphUXihAGb5tUSW489c4M6qcQsWbVntAwidDyl0vfjbgTXaWZa8HbchvFgVSR9IS+xocK+ljvBD4YdD9eViwafhRNep4mBhuRA=[/tex][tex=11.929x4.5]rt8v69t2m131H6e9ZO2kqBMlUTNb5ZJ4RwpzxnjVzwqAj0eDX8Z8zeCZMyLe7Tml1auxy077FMjaLXkxnWZrexVixUdclpO/dZ3gXG5+S/ZZ7eYIirBaFR6iksGToLpj10Gg/egLtoGd86DliNCrdJCYXyCQcScvKXbSK29OwHQkSLPPZgoHYnx/dNeAC7vT/E5onah1/kaZFTHWZSJnmt7MGjW9cReywTh4UUeQ1rE1HMuEBtWL3otYBsPSqc3H3cY2/p6fB57xkGXKCAHFnw==[/tex]即[tex=5.214x1.357]GnbgCTqO/6OsOsCWULk5ityb39/1uDwPsK93wcW74BA/p2DFai943j3hLBASnq/a[/tex]。

举一反三

内容

0
设[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex]的元素全是 1, 求[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex]的[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]个特征值.
1
设[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶可逆矩阵，[tex=1.286x1.071]mcwpV0HZfcjUtysCWsv1bA==[/tex]是[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]的伴随矩阵，则未知类型：{'options': ['[tex=1.857x1.357]nB9mNOUKcr76IIi53ZsfkPx95v3/3E645aqs9iEzs/8=[/tex][tex=3.571x1.5]QSzDgFULXmCzbnmgEKrb3Zn8OXSEBfVdfe5eF4OBDmc=[/tex]', '[tex=1.857x1.357]nB9mNOUKcr76IIi53ZsfkPx95v3/3E645aqs9iEzs/8=[/tex][tex=2.214x1.357]vrsMnV55RRlJmEBE2zosJkkUD5j7cS8a2dnYwhxzauA=[/tex]', '[tex=1.857x1.357]nB9mNOUKcr76IIi53ZsfkPx95v3/3E645aqs9iEzs/8=[/tex][tex=3.357x1.571]7uRzEjzFjrMzO+xZBgb4yXULVEvsDm7HHXd6y2aKp/abu5FwaB3E1jiJHen+pNR5[/tex]', '[tex=1.857x1.357]nB9mNOUKcr76IIi53ZsfkPx95v3/3E645aqs9iEzs/8=[/tex][tex=3.143x1.5]/EaSgzJ4qZa3HYxz9e+RnoxEjoZ/OCot5p/Okz3sgoQ=[/tex]'], 'type': 102}
2
下列各命题中，正确的是未知类型：{'options': ['若[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]是[tex=2.714x1.071]Xa6YzCV9VTlW9p4lLOpktw==[/tex]矩阵，则[tex=5.214x1.214]3chc5CDXDsI0h54V28mcXDjvQbC3Pds0JEMntwGGZZsuKaqGNgx0qTVrS4Z7004p[/tex]', '若[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]是[tex=2.714x1.071]Xa6YzCV9VTlW9p4lLOpktw==[/tex]矩阵，则[tex=6.857x1.571]nB9mNOUKcr76IIi53ZsfkDM2WL8M7oTo8qQ0uBO8xbzhSlLntjsE7+hGHjXSyYdJPgh/PsIMfiUAwasOquZfXkxlJX+G3XuQW4oIXT9TFy0=[/tex]', '若[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]是[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，则[tex=5.214x1.214]3chc5CDXDsI0h54V28mcXDjvQbC3Pds0JEMntwGGZZsuKaqGNgx0qTVrS4Z7004p[/tex]', '若[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]是[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，则[tex=6.857x1.571]nB9mNOUKcr76IIi53ZsfkDM2WL8M7oTo8qQ0uBO8xbzhSlLntjsE7+hGHjXSyYdJPgh/PsIMfiUAwasOquZfXkxlJX+G3XuQW4oIXT9TFy0=[/tex]'], 'type': 102}
3
设[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，[tex=0.929x1.0]v91YW7o9X/DTCaQqpd92VQ==[/tex]为[tex=2.714x1.071]/nWgWZWXmeNCPcwAggrwNg==[/tex]矩阵，且[tex=3.5x1.357]eWZh7PhJv+Do+sZ/H0ne7v+jsOQZm3tyNjPvYFFRhqY=[/tex]，证明：(1) 如果[tex=1.786x1.0]kfuhkHVqbV0IIhrn9d/KMw==[/tex][tex=1.643x1.0]noBwsiY28ExIUpjhfglKjw==[/tex]，则[tex=0.929x1.0]9MCaa3NdBrky4bnBPtTtgw==[/tex][tex=1.643x1.0]noBwsiY28ExIUpjhfglKjw==[/tex]。(2) 如果[tex=1.786x1.0]kfuhkHVqbV0IIhrn9d/KMw==[/tex][tex=1.714x1.0]0XLjAIdr/VWCPpq7m87mjg==[/tex]，则[tex=2.5x1.0]N03YJsyZz2LaYYcYOh9E1eSO7eosTRfeXQPdhYkxY4Q=[/tex]。
4
设[tex=0.929x1.0]JkZEjSnuwtkZlFnZMXvQ5Q==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，且满足[tex=2.929x1.214]vfVZ2jJRqLexUimvCjMPE/6xT+hyy6o+qSw0BucxBec=[/tex]。证明：[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex]的特征值只能是0或1。[br][/br]