试用向量法证明: 设[tex=2.286x1.214]XFQeabN7z0jBrIlKJ5wKtg==[/tex] 三个向量不共面，若向量[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex] 满足[tex=8.643x1.214]pc0d189WKHGaQSOPYulcLmE4eqh46zHXogpUh9o/G48hoPRgmvT3zQuY3+BJXWwx[/tex] 则[tex=2.071x1.0]S58FaUSfom9xiguEYLzV4A==[/tex] 试证之.
举一反三
- 证明:如果秩为[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex]的向量组可以由它的[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex]个向量线性表出，则这[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex]个向量构成这向量组的一个极大线性无关组.
- 设向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 不共面,则空间任一向量 [tex=0.571x1.0]QDHYLzpRIwhOrWBqGonCgg==[/tex] 可以分解为向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 的线性组合式 :[tex=12.0x2.714]EKa3tlBXxUzrZm3G0NxoF4BEV+uQk9RXqZ1Xf9B11fEMxcw7CPLWJYzej2ceFrWCEkxTOfFyaUAzMJbZOHFXTyonbonaBRPx9H1FWIo65q+dtzg9XHmNztxgcnkbq3yq[/tex].
- 设[tex=2.286x1.214]3g6BQlbwSX/DLbvhc6A8PQ==[/tex]不共面，设向量[tex=0.5x0.786]U5O66aolbR1y5vuKrQbXNA==[/tex]满足[tex=2.429x0.786]7XYeXl1HIhWEAH8n0NPBsA==[/tex]，[tex=2.786x1.286]+kIsvNtaVqd85ORmVlVUYGOLGBhRk/og9NsaWNZHRqE=[/tex]，[tex=2.214x1.0]YKk9sue/NX7OEU81UbrXDQ==[/tex]，那么有[tex=4.929x2.214]6cxmpltEh6pW2TWZIEMzX3sVrG60SQdUupvC0f1Ey0Q=[/tex][tex=11.143x1.286]6lhM+ZMhfBEmeH4RJgSAnBR2cFvD2n8HuJ8tNqWurJGUwNyybUdQKyDvtgQJJH5x7ik19ax/iA9bEOjFuwDxfA==[/tex] .
- 设三向量 [tex=2.286x1.214]/Uu9jgxB4g+DifSL38NMLQ==[/tex] 共面，[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex] 与 [tex=0.429x1.0]Q2fWySASH/4Xf2eu85OwAQ==[/tex] 不共线. 证明[tex=21.143x2.786]DrA5hx1t66qUt8yfAeatHZfeS66ayK/g6nl5bEHaWVLXgfarslP95ZD1+gujPiNrxe8ZQw/nnnqBCYE4OnEL6IKW1nIkTOQD2GhbOYzTNcNmpm6DvnESw8gJq5XI4loL2U3NBQjHG7cHpAYxhANDY6KfktcAO33rAkwu7XUMCuBon2aENU5KJnqdQeUm1u8uAB60sdVLDk0TsJubRXXmce8Pl/3rtXUuWntK47GZfXYsKVM0doiIWltkdNgdB4bwvexnBN8pgGPpJ3qhH14FpvC2nKdDKFvX9HF+MCc9OeeakD5QV2omQlpr9oqOwIyRF7jO+FZflPDzndWkQRQjbpsOi2FF8wpaUiKsNHtWZf2dQwvV41o96u5I6uyMvgyAV5Auy4zVT2nILFQ6OnhyOQ==[/tex].
- 已知向量 [tex=2.286x1.214]XFQeabN7z0jBrIlKJ5wKtg==[/tex] 满足 [tex=4.571x1.143]InCny3Wfqa5mNKUEtKBgPb5dscmEBV+E42g6VOSiNE8=[/tex] 且 [tex=7.929x1.357]O8JDLzEyB4ioF4H9Ti+aawNMlV7teUcB8FP9PbzJ7LbTi213lgr9dhSkSafOPhD5[/tex] 计算[tex=7.214x1.286]v05qfwPPJZ8FkDryxTvgcrsEiy7MxylUjlTcujc1y/MdeHTtordv56gYm6hL/eRI[/tex].