• 2022-06-29
    设[tex=0.929x1.0]dOZo8m6M2FCnsdV3AMCDlg==[/tex]为m×n实矩阵,已知[tex=6.571x1.357]MVsnGUDjteIUZsyQP8wk5lDqyxeYWJHlkMfjdD128N1yNmNz9cH4TEr8VKwZJ2LvIP0Q0/vAlTzNgHyHlr+aerUkssArj3hnbhqcO3t/kF2a8KvOf+/NNaC8JAmjBeFv[/tex],证明:当λ>0时,矩阵[tex=0.929x1.0]59zKXEIyJEI6ZiaRBHQzrA==[/tex]为正定矩阵.
  • [tex=16.214x1.786]qLfCK1ZvSHsu4VEM0GGu92BJ7QYotDS3I9A/NM87A7XSOGR1O+7yESW7YDeJ8EUN8B6jFKMuLANgQD5jNiwfgHb9wgMsnMFkcGZMV1uRHRP7Iwd01f5uAe9dHHaGpSOQ/Fd+MaGY0ykaUUyKMzAaFiu1hAxyHWY8bKozF3r6siJC+KISGLu+upfggAuSUYqdSyETMJ/V3dA5f5Ny7Niyp2D32sTXTJJS+XAs73Vbd15vmgXnE3TMEbCiKISrpA+1B0pRgzixEnnkhwl8r4C5aw==[/tex],故[tex=0.929x1.0]59zKXEIyJEI6ZiaRBHQzrA==[/tex]是实对称矩阵。对[tex=3.286x1.214]y4/KIIBME7vp0q+hPv0HynhF5sJDMvTSbquswSh9qAw=[/tex],有[tex=11.571x1.357]/lI35tjgrvHqDGasQT1TGulOjVG0Oq0pN49ZWEfwz6qfKClo2CvwNyFbIb6KuPWV[/tex],因此,当λ>0时,有[tex=34.929x1.571]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[/tex],故[tex=6.571x1.357]MVsnGUDjteIUZsyQP8wk5lDqyxeYWJHlkMfjdD128N1yNmNz9cH4TEr8VKwZJ2LvIP0Q0/vAlTzNgHyHlr+aerUkssArj3hnbhqcO3t/kF2a8KvOf+/NNaC8JAmjBeFv[/tex]为正定矩阵.

    内容

    • 0

      设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]是 3 阶矩阵,且[tex=2.643x1.357]h0pLE8vvleI3SS/lZLfCsw==[/tex],则[tex=4.143x1.357]TzVoItsLVWI00YVI4rvLQQ==[/tex](    ). 未知类型:{'options': ['2', '-2', '8', '-8'], 'type': 102}

    • 1

         设[tex=0.929x1.0]JkZEjSnuwtkZlFnZMXvQ5Q==[/tex]为[tex=2.714x1.071]Xa6YzCV9VTlW9p4lLOpktw==[/tex]矩阵,如果矩阵[tex=6.143x1.357]sb0lI+O+hg9lDaI90Oub4JkVwgoQwUeWOJ5eCSgwqeWiy5uq90e5frG0SZbGhn8x8L+iUg8dSz8qE5s7bm+0UG+nJovMWLop6tcSEeVuHtygXSNTlKd+U8XJKdZ8Qi3N[/tex] ,试证 :当[tex=2.429x1.071]8zpXB85KiofkRevQFrdlFA==[/tex] 时,矩阵 [tex=0.929x1.0]GTnOCR9hNPsOuxGSyBGTAE4D+bwdNZdKWKqAkIkho7A=[/tex]为正定矩阵。

    • 2

      设 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]为[tex=2.714x1.071]Xa6YzCV9VTlW9p4lLOpktw==[/tex] 实矩阵,[tex=0.857x1.0]ubPM9AyoNrlSc0V+wMCCQzy50BdPG4mkARA+lu2reE4=[/tex]是 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶单位矩阵 , [tex=6.571x1.357]MVsnGUDjteIUZsyQP8wk5lDqyxeYWJHlkMfjdD128N1yNmNz9cH4TEr8VKwZJ2LvIP0Q0/vAlTzNgHyHlr+aerUkssArj3hnbhqcO3t/kF0vg//FaNVxv1DI6qwrZ4tP[/tex] 。证明当 [tex=2.429x1.071]8zpXB85KiofkRevQFrdlFA==[/tex]时 [tex=1.357x1.214]A4csvKrMwGXMO83DS3NGNQ3wZ0PmueSDXc7YNJmyLy0=[/tex] 是正定矩阵。

    • 3

      设[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶矩阵[tex=0.929x1.0]ysPsVBYgue2sVzMz/Uq3u0A8rVtfBFebzXef4B7T0+U=[/tex]和[tex=0.929x1.0]lfAzp4E7jz98ZvbLVaeb52L/rf96Vha6tpeJ/pCuQrc=[/tex]满足[tex=5.5x1.143]ysPsVBYgue2sVzMz/Uq3uyTsebDpk7iiBhfQagFxYELnByW7YYGpbsCHsvKGvNW3ynjjf1GCTKOmGNpfywTws7aLsoJBEKNq4NdWKZItSmg=[/tex] 。(1)证明 : [tex=2.5x1.143]r5Haq7W1lVGBc4dFEM2Zk4Xcs5ubhclv3FlkYV9eqtR6YcaA5xYhbLb3ZOyZXvDU[/tex]为可逆矩阵;(2)已知矩阵[tex=8.714x3.643]k4XxnokJDFH17b6cU904x1L+ezwnamK5bBEWCJuqlAqd0xDJqZmPCLpsfN0pzpqWNK/3zauXOc34/6ExNHyRIqyz+T6tEOoZO5gdX2wOPjkuaT+XegBgVBOl93i/nYRCKhASq4FL4+S4LhdFh6VPDg==[/tex], 求矩阵[tex=0.929x1.0]ysPsVBYgue2sVzMz/Uq3u0A8rVtfBFebzXef4B7T0+U=[/tex]。

    • 4

      设[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]阶矩阵[tex=0.929x1.0]zkuxy59wnc0FrSuUc1OFF6pw7am5S+IP5AAfiovVsGI=[/tex],[tex=0.929x1.0]GTnOCR9hNPsOuxGSyBGTAE4D+bwdNZdKWKqAkIkho7A=[/tex]都是正定矩阵,证明:[tex=3.0x1.143]O8o/cZDTF8ipMqduQHBWgi6pxFN4tTQV4LSHcTIya2I=[/tex]也是正定矩阵.