用定积分的分部积分法求下列积分：[tex=6.786x2.786]Xron4GG90VAk3dDkQdPde3H60JfEf5oo8EimMKx2557P8YUPLXBU8pP4VKLteyzR[/tex]

求一个二次曲面的方程, 使这个二次曲面通过两条抛物线[tex=6.786x2.786]7EJHVCtO2IWq3KpdB+jQsk/WqGu6VTn1m9my55ygdafmU5dhXe7Zh4rp7UaHbe8UaFSwoykvdhzuteHxonWl6F4VtxU6IzIRLbySjt/dQA4=[/tex] 和 [tex=6.714x2.786]qKPvVMF+Jw5TQDnDoC3zvydSdyy9B2jHPXbQLlkvE/4a8r+zLbEBFOAaJ6WCmaet6i6IyPVwnp23GQiClAiyoUKovDQNYXHh4RV2tWxr3ak=[/tex]

设[tex=6.786x2.786]3BT1BgBZQ5uJXxD5dg+w29hP8bh7zob8OMKjCfTXxsgtcNV4bbSe1iMacarr9C03oac+Rn4rr06QHA2bDuuftw==[/tex], 其中[tex=2.0x1.214]2UoWlZMHs+82muLB9sdIZw==[/tex]为方阵。当[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]可逆时，求[tex=1.714x1.214]iQ/iEbsDm/5Je+BSznZxUQ==[/tex]。

矩阵[tex=6.786x2.786]lRsc+7xS9mVs48x3DLiOg2asEhVTfp50N5p5QSXNLqmieFRXSBTqqJhWuRQsNSjt4wIkX2rw/c/q57ZeTyN63g==[/tex]是否对角化? 若可对角化，试求可逆矩阵 [tex=0.929x1.214]4M4JO+cg8PL6vWL6afoCdg==[/tex] 使 [tex=3.143x1.214]W4jiGACeVytyGqwMmeXGeQ==[/tex]为对角阵。

设[tex=6.786x2.786]3BT1BgBZQ5uJXxD5dg+w2xB1PYOoHZOhXhLMncQOzCf7EGxpsWgh71ABPE3OvFMplEu6c3rLtMCVWhL9ROMi9g==[/tex], 其中[tex=2.0x1.214]2UoWlZMHs+82muLB9sdIZw==[/tex]均为方阵, 写出[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]可逆的充要条件,如果[tex=10.286x4.786]3BT1BgBZQ5uJXxD5dg+w20d6qzmH0OimEwGxlrBmZIo84lmZvBIXB5DEt/VNsYWOjZ1NdOldl8l9xAniKY/mr5rFW/zG1GSEbsl9nXq3Nj1CnPnKB7FE4upIrpm4Dz8XHMPvGJXI9g8Et4GyqiO1vpCEpCgI4pYLzWEFysOcYTM=[/tex]，求[tex=1.714x1.214]iQ/iEbsDm/5Je+BSznZxUQ==[/tex]。

设矩阵[tex=10.071x3.5]QN0fTQbn6M33pU3gx/S2shauyFS3+ACuvjCeR4/plRK+Ar/k8T5+D2k4F69nSXVH7uae8ESD+UaiI7VoVixG0VymXeWft/sOsGxPdl5v/pbKPjBAtNElsnvPQ7GCxvMejMPGNgxUq5qm9lC+NbypQIdG002sZGhmg8RjTECJd4Nkex1fdMAXGfHBHtZmaU/8[/tex],[tex=9.929x4.071]opqi7S5YyIUs5JQiNQr2vNAXVg3BXAPxe7wSDgfNpByPjU8aoa+gUU9+XxBepbwpY5YfaK+O+K7Az7Isl8btr7auYxcZu2Bzrsm3oUfVg4R4dA8n5bqKcyiT98HgWFGZDAxY7AlD0blNlIptqk3n8LSdbwhkQ8XR1ejaU8NF3e0atZDHaDpieF3QihxUwe4X[/tex],[tex=9.786x3.5]2dkVCjufgjJKA1Jpl3dseuOZzowpS59HPk22eBA0xFhE3jVpCdEiJMxkuq/nF8I8rsspwhAqETkLr1p43WewcHej83ez13fmKNnwkQdpCeav/aTL/ObkfGVpxYvxr8WjhRMGEW7jTh3QgyICQVHWaPXHli1mn9ZvlJFc0qkwMrqAbD2Lc8gRH9Dxy+sJsRRu[/tex],若矩阵$[tex=6.786x2.786]cUyiQVfXVPAX7qbpaubKY/kSim9pWfxGB/6NSsnRGj8ldNZiffB5gl73zp3KMiI3qe8xcwvZ8Gq4Bn2EpdK6UQ==[/tex],证明:[tex=5.071x1.357]E3Rcs/uaZmoNBP9KoeiSGieV2Auo9jOBRkM8qsuc/dk=[/tex].

设[tex=0.786x1.0]kEam2pLJe4uAYVdcny2W5g==[/tex] ,[tex=0.786x1.0]EsJDtGYVBcAkNM+hi9jDJg==[/tex]分别为[tex=0.5x0.786]51EIYuoXo3UTYashe96uEQ==[/tex]，[tex=0.429x0.929]SHDYlnTnnzxVv4clzlq6TQ==[/tex]阶方阵，令[tex=6.786x2.786]jRfGsnrf6b2OkLA4NcoXOrQf/R3DSUHRdIbB0vuYy8VVG4mQoiZfm/8DsOr0axTX61xDmBaSJGQKTtjwM5uTDw==[/tex]。当[tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex]可逆时，求出[tex=1.786x1.429]36D/H6uaA8wQM2NRdVsXLg==[/tex]。

下列变量组（）是一个闭回路。 A: {x，x，x，x，x，x} B: {x，x，x，x，x} C: {x，x，x，x，x，x} D: {x，x，x，x，x，x}

以下谓词蕴含式正确的是（）: (∀x) (A(x)→B(x))=>( ∀x)A(x)→(∀x)B(x)|(∀x) (A(x)↔B(x))=>( ∀x)A(x)↔(∀x)B(x)|(∀x)A(x)∨(∀x)B(x)=>( ∀x) (A(x)∨B(x))|(∃x) (A(x)∧B(x))=>(∃x)A(x)∧(∃x)B(x)

以下谓词蕴含式正确的是（）: (?x) (A(x)→B(x))=>( ?x)A(x)→(?x)B(x)|(?x) (A(x)?B(x))=>( ?x)A(x)?(?x)B(x)|(?x)A(x)∨(?x)B(x)=>( ?x) (A(x)∨B(x))|(?x) (A(x)∧B(x))=>(?x)A(x)∧(?x)B(x)