证明：矩阵的[tex=0.929x1.071]GF6lPkbwM1/sKcTXI74B5g==[/tex]型初等行变换(即，两行互换)可以通过一些[tex=0.929x1.071]buZKswv8GSg4ZQySlQudzA==[/tex]型与[tex=0.929x1.071]9/ixLDjuSXaJpaOE7n+RlQ==[/tex]型初等行变换实现.
提示：[tex=31.643x8.214]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[/tex][tex=21.286x8.214]hfx3NW+kCsKg1ptCHak5gjX8FiUXwpsWPRGWOeO7kTi5RRTgKql4f0g/8gtb9WgC0l4R1YgJJPJkGAVpOakoer6Cwl7wGdzQymz3K+CTF5jNSz9nJ5AqJ7lqtVex1VBu6yKafKazte6HDx+XLWxfRGY0Zv5MGWsU7tivsskLNGSnQpA4PuGlN0FFY71FXURBsS83ehco0M9Ok8xhChHHu6UI2b0UlWfocC0K07c/IejkClBTbEx2dKHR1z0kQejLKcv6TKIwTgxc0FzXOrioWgVXFyE/4Cu31AQNqNZ317vbbGhn+0Qf3GKQWE2qiTS+mUBW+Cd3aD91D0fNRnr8ailyEV/YAiCDeVN9SZwGSZ+bzVqLtqxqEviR5hbfXAgEhwLOXzcVyS4El4lfo/MJsMlruu4cvbHuglCIvqiqH5E9qvK/QCtDdhj/vQCMY+m7ohYgC7nb5qxmTU4Wzdlryss7J6HtKr4PRMdGC4aBALR9H/TjkUCgo1RWOZxl6gyZu9jBPTVmILwE+jSZ1cxRU0ahzf4l9bKb3loadr8rnhHVlGoj/b/jvdQpZRX1Xbu3QfLKeb3Y+oKcU8x1CxO1eK6VYUMQ5i8mCUyzO6iOgQI=[/tex][tex=14.429x8.214]jlHcQTgl0LNq6emDl3ij5m66KQx79r/EjgKrADzB2h+an1BfJdrH8OKURKyjILrppMaBxVEGSIx41vdXE81T2TXDW8Jen2aDbBLp5P2Wj5aNEdhdhCJeqPWbRuxxK086OgKAQ5J9c+rovHQAXqodLw1/z8YaKxNBUuUSkEwQroAMaFbck/hfCQDRMsHOy78AvDJC0zoW7JUMGh/QJR4OXmEmfjZ/uPGm2Gezu9rzLmQR3CLG4M8UP1XwEt/+v3lfYEUqw5y1SIKegT64lF/t2Ah6W2atGEHQ5mQ9rNkZNIvghx8LU1F+jAEmhz3A2/2xt3j48c64wdK8sY4VP/eflpuVCDKs+VzaaPteFsgeZt+WKg2nNgSFjO6/ifQ4gfsskW/KgabnA2QuGVRu2bkc7WTSnfarZGC+nvZHW84hPxb7ca3dZiDzJlf2nw5bqqhI[/tex][tex=16.214x8.214]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[/tex]
举一反三
- 证明：矩阵的[tex=0.929x1.071]ye7wVa6THCKv06rO3baM9A==[/tex]型初等行变换（即两行变换）可以通过一些[tex=0.929x1.071]502A3kM9YE+9j/2noEqw2g==[/tex]型与[tex=0.929x1.071]vxzTVGpzraNdAfUuV99UxQ==[/tex]型初等行变换实现.
- 用初等行变换将下列矩阵化为行阶梯型矩阵，并求其秩。[tex=8.429x5.929]dNSDn9BXm1mpm241IkjqDK1acarp7uEXzYmuVtT7iZZFMMQad53UarVdZOO9LaZclqqiQ+Dr+Zs3UUZe2HPgYmFX/TPm1+WolZFZGBdtfN6KHLQE7oP1GphTOG94oqmPX7zTVY8d97MqHXe0iKz5nomJhQqqkQmREGpHhuJgR1g=[/tex]
- 用矩阵的初等行变换将矩阵[tex=11.0x3.643]C3i3DfkQVo2pOvnj2q0JK8uICAslAc7H+uBU3eOkL5pCh0WRibyvhHMij2q4oiCh39plNQtM0tbVoTgWEIcmp+mHwbWEs3+CB80KUDM4ZsK939VlOjBlhOojGwiWdWFZKz7Z0OrHJSXDoUsh0bza4A==[/tex]化为阶梯形矩阵。
- 用初等行变换将下列矩阵化为行最简形矩阵：[tex=7.857x4.786]jcCMHflCR8OS9TosV6N5vE+ILInEdrNZmLPdu5yGc58x2ThFgeZlIoX9A7qb/G3BsPqADtaTucfoTIvayBE9mmX15MEqtmh5xctTqssz6rNbFi75UX3kKIcBpUtwLNzB[/tex].
- 利用矩阵的初等行变换将矩阵 [tex=6.5x3.643]NeoTBlf1CmkUoMf07Si5dAD8ZbdksGO0fA9hs2XXNUaQJ6hik+QdSdzXXL7Do2ZtpnsSmK0ZLOe+TqTc8cQQL0vYoBA6XmfXeaLwdFf/3Cv4X/cEuPU+mDvs22bLGJ6N[/tex] 化为行最简矩阵.
内容
- 0
利用矩阵的初等行变换将矩阵 [tex=8.214x3.929]NeoTBlf1CmkUoMf07Si5dEcn2TG6zebvt/5RMBtlBueOLdtecTu8sHIwlVvCx5xG1F3wf+1E2WFPxgaat9EEH3oOxiLDDIWQ3X6tmhQVoC+upxaIXeHCGW7yzZR/s3d3[/tex] 化为行最简矩阵.
- 1
用初等行变换把下列矩阵化为行最简形矩阵．[tex=7.429x3.643]sqT5ECWErx9+sgJ2TkxNkeXrph9cFwwkrb/Ve0fwplRwoOWSteVt0MQptyeDl7tabfUIP1Ppbv+4YDZM3alBASLCdpsfhgsZEOh/LzWOnQU=[/tex]．
- 2
用初等行变换求下列矩阵的的逆矩阵[tex=4.5x2.786]jcCMHflCR8OS9TosV6N5vB0YNYCYNNOTmW+/Xyaeog6rA0KugjnCjJY4NVvcov0ChJerMdjoodQRv4TpwwBfWw==[/tex];
- 3
用初等行变换将矩阵化成行阶梯形矩阵和行最简形矩阵：[tex=10.071x4.643]jyVOORWehIbTNQvvtYroWhAnO4BdeUQ1K+KFAzZ6kNqqM4oTf9cXDU3iLd8UpgF6ei0xOjfm6CB8kz56NQJsABIayYyDkficxS2Jdz9Z0eNLOWpp4CaWpz6ao+UVAtgMbbHExKaJPWN8FeB0ylKUWzdGT4GF4yOH8DTEifslF8tXdVrAMorDeFLmohdgLnor[/tex]。
- 4
用初等行变换求矩阵的逆：[tex=5.714x3.5]De166nmeTkb4C/83+ZZH22dbEjNKrnjmBwm3Jdmz0JML6nfyM/ZKF88uPi11IaLL8LZKvSsUZfWX+2Ur3zXuLOHTRCdjXg9pIa5p6FrrHkwt50sAssx/Pxrmf5KzIrOp[/tex]。