• 2022-06-06
    证明命题:若[tex=2.286x1.0]oBxHqaQPNIcRDnRpE46qdQ==[/tex]是同阶可逆矩阵,则[tex=5.786x1.357]cRSSutUe8lxP7o+KrExJjK9oAJrSiLyeLoTYwLm8SsY=[/tex]。
  • 因对任意方阵[tex=0.5x0.786]hycNLgozeED/VkKdun7zdA==[/tex] ,均有[tex=5.786x1.357]rHvVEgqZfAiE8vvYLbD2+hG9kGYNfAzAW52aNZpyskY=[/tex], 而[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]均可逆且同阶,故可得[tex=12.857x1.357]0tYvF2oMI2yu27kFYJxjs5EKdKjNdP0/UZ0PprnBLeWZvQ7q8g8K7a9I3r4lpCuJEvpRNzcxSdtT+7lrJaIUYw8Zxur3xmY9s9/dqPxf4+8=[/tex][tex=16.857x1.357]tn5jLf9cYxC2bXEYVSsuvVJIxFgPebJmQFay2QmVHBk5lXNW4SpPvC24Mh0+p5RgA6IEwnsru+W0ceDk6K80vbjnMu0Nq+/MbNAhsdhKWiOBaKyYKWjbI+/HWaSjJsFM[/tex][tex=14.5x1.357]LIZB29zlmqUlnEl7wqByczIEI4l+WK5KT2oGpW4akvc8xCsWABHkvrSrFlPxgJZvxqS9JVSGDs0OneHP1S4cDw==[/tex][tex=9.571x3.071]CeOWlpLvH8Qhk/RmfIvBHaXSOEI2f7fF/hhQSXrjNuCN23bgeyiAArpb3crfMeUdUGTyR8jycFmZNmSLwLzKaJ4QDTc2zue722BVD5ih6B16PbkZhpQlGY3KMvHWgo6eX6otSnWAp/S4qUQmNj4TAg==[/tex]

    举一反三

    内容

    • 0

      已知 [tex=2.071x1.286]Lw1m7LuL1SjurX1WRZuPUg==[/tex] 为3阶矩阵,且满足 [tex=7.714x1.286]ThWWPhndKkz3UClWdkawSBreeT7S5i5PvnTbUSWKYOOv9U2rV7yWwLvdAXkYzsfH[/tex],其中 [tex=0.786x1.286]KdMX/vrMoFuyctoWaUWH8w==[/tex] 是3阶单位矩阵。(I) 证明:矩阵 [tex=3.286x1.286]7/dUziihQFEuopQUmAB3jtRjn7Bmun7c4UQbytj87b8=[/tex] 可逆;(II) 若 [tex=7.571x4.786]174MZEe/izWSafpCRvJbd3cQKHCzrrjGGKpSfjzsHHVXpVP4uwNKwm6JKWYSK3g5xlXwIaRNk+2zOOmSaTeVcClZXyEuVtudF/ZEztSsKpA=[/tex],求矩阵 [tex=0.857x1.286]BQkHOimMmPUuGqQUunHC8A==[/tex]。(本题满分6分)

    • 1

      若[tex=0.929x1.0]TCJ8vORtSoh7E6xiLKJBSQ==[/tex],[tex=0.929x1.0]k4XxnokJDFH17b6cU904x5y0XoeEFbvPcEEIqbrGwnU=[/tex]均为[tex=0.643x0.786]FU7w6l1IEII0B13k5eE1RA==[/tex]阶方阵,命题:若[tex=0.929x1.0]TCJ8vORtSoh7E6xiLKJBSQ==[/tex],[tex=0.929x1.0]k4XxnokJDFH17b6cU904x5y0XoeEFbvPcEEIqbrGwnU=[/tex]都可逆,则[tex=2.571x1.143]r5Haq7W1lVGBc4dFEM2Zk1W3v8ag3hQ/jxq8jI47ovMRWPbY5eGp58IqJCI62D0L[/tex]可逆。是否成立?若成立,给出证明;若不成立,举例说明。

    • 2

      设[tex=7.071x2.929]r+tiAx6ClSaeP7cZbqpjmXACNCkTkLbXSmdm65cOw+XEpcgk96uDO4lIHcqlGaczSOLNcuYH7zqrd49WI1GD1U4kYe0GU4X7fhxjEj8PY0o=[/tex],其中B是n阶可逆矩阵,C是m阶可逆矩阵,证明A可逆,并求[tex=1.714x1.286]TO1yVSeu6VTkH5eqe0g3AQ==[/tex]。

    • 3

      设 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 是 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶方阵, [tex=1.143x1.071]DFelGZAPNOqMgdbfKVoEHA==[/tex] 是其伴随矩阵, 则下列结论错误的是 未知类型:{'options': ['若 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 是可逆矩阵, 则 [tex=1.143x1.071]DFelGZAPNOqMgdbfKVoEHA==[/tex] 也是可逆矩阵', '若[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 是不可逆矩阵, 则 [tex=1.143x1.071]DFelGZAPNOqMgdbfKVoEHA==[/tex] 也是不可逆矩阵', '若 [tex=3.571x1.357]BIh93n4rr/VbrKyEAPPe8rDj7DFYI+OK8rT/Ls1y1eU=[/tex], 则[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 是可逆矩阵', '[tex=4.571x1.357]cnY8hKVKlPTpxyphVsUxyKhjkG54udEhsO0bBHAuhUM=[/tex]'], 'type': 102}

    • 4

      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}