设[tex=3.5x1.214]USrgmNmEfxEBQ6LPH+RsDUp+8qne/bp9LfY9FPqR6z8=[/tex]，[tex=4.143x1.0]k8PvTJe4iQVkvPfhUhxDGMhjLthuBa4S1gJaK+DK72A=[/tex]，从矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]中任意取出[tex=0.5x0.786]BgHR5DBWke5rTEC5XEckiQ==[/tex]个行构成[tex=2.357x1.071]0nq0b1fEFW/AV6tuzNPMsA==[/tex]矩阵[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]。证明：[tex=7.357x1.143]uqh+oOvD2P9iqZ7dD7XO1GZ5XNhSJjjkU/76qu4Xc6GwVUDWSkCTCahLLCul1KbZ[/tex]。
证：设[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]是取自[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]中第[tex=5.0x1.214]Pr7Usc9o4i4z2PgdbBVap8CYp8Uv1+996X3n5C4nJJw=[/tex]行调到第[tex=4.357x1.214]cspBT75m7u4ay7focI4N2CI3E6ZjxCKnXJkmoMtaNgM=[/tex]行，得到的方阵为[tex=5.0x2.786]XbmfowmH+x2njRlGmJod4prjdyInlqC2VzzkOFWhlarpWO6rmGHnOa0O7sm8jGNqBKBWiTI27sm/xAmrIkbA2g==[/tex]。由于方阵[tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex]是由方阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]经行的初等变换得到的，所以[tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex]和[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]是相抵的，从而[tex=13.143x2.786]k8PvTJe4iQVkvPfhUhxDGP88oXogRGyA2rerMTpPqSeuV/rukL6bN3dKYSXsw5C+4K0oyZoGaGZ7pZXy/Ocu+hYZTK/8GDEsLWSQC1LByqLbBpwwCcRYfvNElSJA8w/LN3u1+H/fPYuQFxQteH5RVg==[/tex]。现在设[tex=4.214x1.0]uqh+oOvD2P9iqZ7dD7XO1Mm7PalQV6OE5w0Bt1mbZ2w=[/tex]，则存在[tex=0.5x0.786]BgHR5DBWke5rTEC5XEckiQ==[/tex]阶和[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶可逆方阵[tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]和[tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex]，使得[tex=8.643x2.786]43lwIB88E6YnGwCbIJcfhh9a26kCBJIr7uAN5WdCZn91eXvWjiXaUj6Xf1OtfC6Nt+cppqakOM2y9CkqdUkc60an/na4QWDKU5KuBoZUgpc=[/tex]，因此[tex=29.857x4.643]075gCzZzsMRb6HYXYk9X933jAJ0cIQjSEa1tGci+DsLOMKbIfAu3LuKcaK+yLhh+/IH3SrbtFNjDmnNsavSF0dCBqvuMJvhm7WOMhTkuSadrqhn8U8DkudUhV7lPaH8EyJrtvdCbBRp6BWWmgNEtB3WZbHyi4FeiSQ7XVZVCFzC+1sLEhCTNgMg63AmyAOG36E2x3+zMQdD3yXqij8zUJsO5fjktBivemAq9c7vq7NwihptP6viF0gxTj4HqwvCxVmV+++bOKQoCmhwQLfVxsaYPWPHPHL8aCi59hTY9wSrvX3uBgGg1y2uYQfcUzWAriLZM8gQVJRnsMCWzNGp2aONIoGQLt0NV0/lXZK3eo3K2Kp+brePUtwyGat67k+3RlPDyWcFtgEW5VIroX63Qa2KrVrIxHMTSilRfc4JN0pM=[/tex]。将[tex=4.5x1.357]k1XGr7dS8esEFTWkkTX2hs9DSHvb/Aowy341urJCgvQ=[/tex]矩阵[tex=2.571x1.429]MWNSUzOzeNdni+okdnDKeQ==[/tex]分块为[tex=3.357x1.357]bY2e3pU8a38NUdHE1E25hzlqGopxrXZVrLsreCJZvGA=[/tex]，其中[tex=1.214x1.214]Ho8mAPpdke4daIdB3oO8tA==[/tex]是[tex=4.357x1.357]XhGDsKz/jg2/PekyBg2fIpAMFYI25hVHcoGwqMNcpg8=[/tex]矩阵，则[tex=12.929x3.357]075gCzZzsMRb6HYXYk9X933jAJ0cIQjSEa1tGci+DsLOMKbIfAu3LuKcaK+yLhh+/IH3SrbtFNjDmnNsavSF0dCBqvuMJvhm7WOMhTkuSadrqhn8U8DkudUhV7lPaH8EyJrtvdCbBRp6BWWmgNEtByJikexhuvup1QpnFW167mE=[/tex][tex=20.357x4.071]ZGTtUfVHiJDAU4i+qE4bMp+AUYj14iE5+RnmavPuWf2IDfSIVD2qH0waX35zMFwSeBCGQkzisVb0wYgxh0GQDHB3lQEyZjfSwmwa3DfruNe8XhFD0y7jEoJh1diODVLUuvIbV+3848rcPLP7MdxiolDySdCiXkMA5dmA5xk+TvYTD/dODJ8senrUPZZGdHLmwnfQLBvfNmotTuD2n0RpcqGNAgBprDb5AQ4VO+swt0+dyu130tHtHFFG3UQDuNkKeksAQivkTjexMco47Orfng==[/tex][tex=7.286x4.071]ZGTtUfVHiJDAU4i+qE4bMp+AUYj14iE5+RnmavPuWf2IDfSIVD2qH0waX35zMFwSeBCGQkzisVb0wYgxh0GQDHB3lQEyZjfSwmwa3DfruNdqdGI+OKAmdGj9Lec/DNh0[/tex]，又[tex=24.357x4.643]075gCzZzsMRb6HYXYk9X93a1pO9TJkDy9YKrlTC4QXVWU+0R9qGiKcTK6GUODov9ULMQ1whZKDLajy5G8ogNrG7GS3OwAfkhwAaqJONr1aJPYPhJTvtJH82zVGCrN92mux9M6BLpPaLTEhiLBEEZQm3tZXdxd1uxiG2o76tUy5/BEEBb9POg4n5OGCeKCcNdrQ04i27kn8qFdHDwQLxDLVcr22w+yyYrhbGvmzBWCq76k8EoXvuVDWc5cCy2lGQC8LhDd687TtEKXRfGR/+5308Rz/oRogBD9/6svw3ZivI/6hwuHpNiB97/rP1UW9ot[/tex][tex=7.286x4.071]ZGTtUfVHiJDAU4i+qE4bMp+AUYj14iE5+RnmavPuWf2IDfSIVD2qH0waX35zMFwSh5p5j0ICjPO6WOQzpcE89Kdt9GTVUa35bVJ3fUkLQnE=[/tex]，而[tex=35.071x4.643]075gCzZzsMRb6HYXYk9X93a1pO9TJkDy9YKrlTC4QXVWU+0R9qGiKcTK6GUODov9EmIi2t2wzDErv03x6Pgd1rKz4IEk20IWGmdReef3A7w4i7feC97BPK0xrXDKtYc0L3oYbE/SRFzElnPCotlUJ7l+3Dynl4BjlklJqSsyYugyDdIBm8oCXFXSxsLvCwDaWf8xpjpXJhTBIKAi547yWX1EeqtYLRaUTDoajmc3ynClCXRRlvpaY8mgOxeSYM71RNlN1fOKwdT7eKQGtoyJnptA2uhAqqh4TdZhNKPnbOP2P325ZWno+RwgnwtS7vGest7HIhAshrsQwcGcuHhcPpFX0zIfsqRLrOCIywI5ynRfOMTYjHjBKlduI0Fm8uxAIkPU0CHGQxJ6Et8644IPOmelYgFHVyfwk61i7oJJR416p1mqctVb4pdWvXenUtj8[/tex][tex=7.286x4.071]ZGTtUfVHiJDAU4i+qE4bMp+AUYj14iE5+RnmavPuWf1fX5boDikuRftEGyBMlV8lUf2DOOsYE1El62/EhLmOQyiCSBy2f7BtTy+TBMs4pGo=[/tex]，而[tex=10.643x4.643]075gCzZzsMRb6HYXYk9X93a1pO9TJkDy9YKrlTC4QXVWU+0R9qGiKcTK6GUODov9EmIi2t2wzDErv03x6Pgd1rKz4IEk20IWGmdReef3A7w4i7feC97BPK0xrXDKtYc0RLQou5PIew5gUooXGMPmEA==[/tex]，[tex=11.214x4.643]075gCzZzsMRb6HYXYk9X93a1pO9TJkDy9YKrlTC4QXVWU+0R9qGiKcTK6GUODov9ULMQ1whZKDLajy5G8ogNrG7GS3OwAfkhwAaqJONr1aJPYPhJTvtJH82zVGCrN92mxIlZTiuEfT7AUZx/FFWaEA==[/tex]，[tex=7.571x3.357]075gCzZzsMRb6HYXYk9X933jAJ0cIQjSEa1tGci+DsLOMKbIfAu3LuKcaK+yLhh+/IH3SrbtFNjDmnNsavSF0SEjS9ml9oNz6lHMcDqzuD4=[/tex]，[tex=1.786x1.429]VRf9CZOopgVdrUusaxC7Gw==[/tex]和[tex=1.786x1.429]VRf9CZOopgVdrUusaxC7Gw==[/tex]都是逆的，所以[tex=18.857x4.071]k8PvTJe4iQVkvPfhUhxDGKDCIwFk/NOQPo4dToyCuaHW03RZVH2vt0pRPON2iyTlTj50gUP9g+Lo/cqGOY6XADTgoDktH7uK0zBsMzB8+BuZtgTe4EsnwQZv1yr29oit+QAXjebl1oxQbRZFDGi49pBfagyJv2ZJT1XU94SvOOPiWWdmEGiwCf/PFC4JWMcuS3I+eeA9Q2cNIpqeTj83ZfzhV9sgEDxbLHhCAeagBASCHAbwUyk7TEbVEsnKpqRU[/tex][tex=8.714x1.357]QCnSjjZlkUmH/xR95KIndu7LQ7zcxb9GmoHZUVEMbEwy9Wq/RkTJHe22HsLY6xgGweNkRP0rjnISiHoGoC+XKA==[/tex][tex=13.714x1.214]WGcVQ7SjVsMQ8F8UsWKAnsZaKS3E2fcQlxyRuyWytmFPzbUHzifdAjci1iFRV4eKW8EG7iRPnNG7LUQWbSLeve6xKbJp6N0F22bHOBoylsU=[/tex]由于[tex=1.214x1.214]w3UCvqjM/wRFMriPRfdAww==[/tex]是[tex=6.571x1.357]8du80NaDKoqv9tUlySaSoqwvh2MCiw1CtkxBX18z7uo=[/tex]的，所以[tex=6.5x1.214]uqh+oOvD2P9iqZ7dD7XO1BHUGkGfAHjKsd8smtmaDtPJ/AexjIM14d/7apKOjwrs[/tex]，于是[tex=9.786x1.143]k8PvTJe4iQVkvPfhUhxDGIQcLhrYIvCUjeUDPZwyUQK9gU2aP63t0/tBfvoy4cn8u875DTeL35+08GTeQYvkXw==[/tex]，即[tex=7.357x1.143]k8PvTJe4iQVkvPfhUhxDGOwaNnkZqgQUgIJdIe4RTTOuuVBCh013RwK45ivZ0Ue3[/tex]。
举一反三
- 设[tex=8.357x1.357]XaUWLAEMGN2tBYX65t8ll4WpKi48pgDE3ZU2R6SrgnIGQctOpel24pROPa4L5HpH[/tex]. 从 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 中任意取出 [tex=0.5x0.786]BgHR5DBWke5rTEC5XEckiQ==[/tex] 行组成 [tex=2.357x1.071]0nq0b1fEFW/AV6tuzNPMsA==[/tex] 矩阵 [tex=0.786x1.0]ri6gmnf1+J9dGqG5/1sV6A==[/tex], 证明: [tex=7.643x1.214]k8PvTJe4iQVkvPfhUhxDGOwaNnkZqgQUgIJdIe4RTTNGk8EFtiHnt2Zd6yTQbq8j[/tex]
- 设[tex=3.643x1.214]k0VQBkegJwBLxFCyzpXPSExN+eJySm0BJZ3gTKl3sZk=[/tex]，[tex=4.143x1.0]k8PvTJe4iQVkvPfhUhxDGMhjLthuBa4S1gJaK+DK72A=[/tex]，从矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]中任意取出[tex=0.5x0.786]BgHR5DBWke5rTEC5XEckiQ==[/tex]个行，[tex=0.429x0.929]gQzDwVIykgengUJAyMAHkQ==[/tex]个列上的交叉元素构成的[tex=2.071x1.071]mDnbCqRr1pH68nnnIWoqpA==[/tex]矩阵记为[tex=0.786x1.0]9uq8NvjklzVl/yrUHrVKTg==[/tex]。证明：[tex=10.143x1.143]k8PvTJe4iQVkvPfhUhxDGCm2mDu7pJ4fy9DzHLJfcf68ca4DFTyFoO041KY85XA/[/tex]。
- 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 。
- 设两个相互独立的事件 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 和 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex] 都不发生的概率为 1 / 9, [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 发生[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex] 不发生的概率与 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex] 发生 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 不发生的概率相等，则 [tex=3.0x1.357]PlWNHdSuVTfacbkTVT1WGw==[/tex][input=type:blank,size:6][/input].
- 求解下列矩阵对策,其中赢得矩阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 为$\left[\begin{array}{llll}2 & 7 & 2 & 1 \\ 2 & 2 & 3 & 4 \\ 3 & 5 & 4 & 4 \\ 2 & 3 & 1 & 6\end{array}\right]$
内容
- 0
设[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]满足[tex=2.714x1.214]rPRBSosCEth94R4jBBpQCQ==[/tex]，则[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值为( ）。 未知类型：{'options': ['0', '1', '[tex=1.286x1.143]AcbURnSUksMF5caOSz5CtQ==[/tex]', '0或1'], 'type': 102}
- 1
已知三阶矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]的特征值为 1，-1，2，设矩阵[tex=5.143x1.357]GXZk0g8n9F5fV4GyCGm9mygQSr4Yd8XrtrSrBIW9ziE=[/tex] .(1) 试求矩阵[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]的特征值; (2) 问矩阵[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]是否可以对角化，说明理由，如果[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]可以对角化，指出与[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]相似的对角矩阵.
- 2
设矩阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]与[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex] 相似, 其中[tex=8.643x3.643]3BT1BgBZQ5uJXxD5dg+w26muwh1xN1sRXO8Q3eF5f+iTpB6kD/3/7F/Sewwa3hxWs7TCQWFyZq0QSUW2LGcSxj3jay92Ev0sXUjwbpJxe2w84vpk6B1wjRlgxeXY7DUa[/tex], 已知矩阵 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]有特征值 1,2,3, 则 [tex=1.357x0.786]C5gMMrS05DsgTY0BSnf1fg==[/tex] A: 4 B: -3 C: -4 D: 3
- 3
若矩阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 适合 [tex=2.357x1.214]7q0oZJE3JAfWae2ZKHZKIg==[/tex], 则 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 特征值可能的取值为 A: 0,1 B: 0,-1 C: 0,1,-1 D: 1,-1
- 4
设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]和[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]都是[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶矩阵，证明，若[tex=3.286x1.0]B5kng4RQ4+wxoF4j9jMkfg==[/tex]，则[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]和[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]互为逆矩阵。