利用施密特正交化方法，试由向量组[tex=5.643x1.5]spsZ+rMIOMiqBxP/ZoH2F8DJTKnMG2tFqmNYbv87xdjHxwWBuHkB89tv2YZIrVXd[/tex]，[tex=5.643x1.5]spsZ+rMIOMiqBxP/ZoH2FzuS+sLFZBUhTXxdS9ssWxLD2HZfBohNqwx2hH5TIuki[/tex]，[tex=5.643x1.5]spsZ+rMIOMiqBxP/ZoH2FzYz4+Z6GRmmRPLTSJPGngFVfFPEhk8tBhvTpybXnTwj[/tex]构造一组规范正交基．

给定向量组 [tex=5.786x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrZHz3E/QnslgupQMek94C2xenjlUkzmA+m3IWuPjkJUlYmntNcmdcAOej6kavvMFDQ==[/tex], 试判定 [tex=4.286x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrWhfdN8VXI6DbC98ejmhFVs=[/tex]是一个极大无关组，并将 [tex=1.143x1.0]spsZ+rMIOMiqBxP/ZoH2FxD+XO8gT46J4K60j6LjCVM=[/tex]由 [tex=4.286x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrWhfdN8VXI6DbC98ejmhFVs=[/tex] 线性表示：[tex=16.929x3.071]tOuhNvizKyRZPn+XCdGxL6dbNGKzH9GSMkHoE1aX/I5E4wMlnlHQiyuULgtV0e5uMbPX3yKPONEolz6z1dUL1fqxh+ftaklu7p5azbVYvf3JL+27442OG+Fmwy5e2mpuM1W6hEQHXiObuaF/7KygrDjwiM3wPIhiqwQxbPIEAmtLcfye8IoDSuFNW/8fKFgGt6UdRnPHqxgrJcuw0Hw/eHF8PPFUtp88aY5mzIJUDWrAZDxwAa+2+yFyUsXeYdov[/tex]

[tex=28.929x1.5]spsZ+rMIOMiqBxP/ZoH2FyNZ/c6jYvX7C5JjLm7JZ2383xLjBqPRadRDhKeHI7wuT1hqfVIll2zQxUay2uQng8zNheFKDQ3xWNSaadBSmp2M01Y6guPXMV89hVH83eaC6I9GqBJIOrrHbyUHm+q9qml5A0GvInZ849HOyDd4+XrtIbJAnUanc9RYDYFJcn/2uaAOt1RL6PqdlGRYZEcM6Pvq3zdRreXGExf5k7yMc2GfdUJgbGjG+txu5tItCBz7v0vNX4GpQQKxib8vpdbDeA==[/tex],[tex=6.571x1.5]spsZ+rMIOMiqBxP/ZoH2F8nrAwUHVV+7SOpwS3np0tKGDs3w1W2ApwJErtnMJL+H5pNe/zSuIRcWLo5x4hplag==[/tex]。求一个极大无关组。

已知 [tex=5.786x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrZHz3E/QnslgupQMek94C2xenjlUkzmA+m3IWuPjkJUlYmntNcmdcAOej6kavvMFDQ==[/tex] 向量组线性无关,则下面向量组线性无关的是 未知类型：{'options': ['[tex=15.143x1.143]spsZ+rMIOMiqBxP/ZoH2FxlM2xUFnc2Hj3bvu5m/mudB7whlOZ3wlKfslkPMfsOXUFyJMc2q3digbRlJdAr8rZljTcwD1LsTL5coe76XOgSZiyj49Y2T+9bvWkPhu+rKH2rl2Knnv3QEFvAoemvo2282/icESOtq3wmBhGb+BpzZKYrGelSc675myeSTpf2XG4/G5BUH76xegKrV+fGqvSdq7ttiv6cOWUPAGbDqQX35OlFEzCIIlG3nEaozQ36BwqpClOLNwj2kzEiir3cejg==[/tex]', '[tex=13.357x1.143]spsZ+rMIOMiqBxP/ZoH2F/VOxPOH5QMy8Q0uaj2AHmCOQhiltD7ENoiV0PkoHdPA/bo1dorMeUnUYaTxAFih/6u+Rp296HM27Fbv78ePOL91jUMTBWP5W64xHRwP9Gb7EyjzlLXkB/wGiIjy8JeJONyjq8EMlqqyx1/csodtaSV+MBfrBXhQOarlpTVUBAWCyOpj7EnVQHdlxUY2kr1cNv/rD9yP/3a6Jq9PoZ1krEVj6Rd565Jxx19Mupexa/5puh46MbZCrbAaTxtQz5ki0A==[/tex]', '[tex=14.286x1.143]spsZ+rMIOMiqBxP/ZoH2FxlM2xUFnc2Hj3bvu5m/mudB7whlOZ3wlKfslkPMfsOXUFyJMc2q3digbRlJdAr8rZljTcwD1LsTL5coe76XOgSZiyj49Y2T+9bvWkPhu+rKH2rl2Knnv3QEFvAoemvo21KbzqnFWBa5uEYKx4dniHKkbgH0RaI82hNcVEa3i/AbNnkOyPJLh065n5YniyHVM1703vR3VRQsOKJBYhpyeYLojeHCpHOeSBPxfmsTy0rzCHYLVMmaVXcbHzzJDuG+lw==[/tex]', '[tex=14.714x1.143]spsZ+rMIOMiqBxP/ZoH2FxlM2xUFnc2Hj3bvu5m/mudB7whlOZ3wlKfslkPMfsOXUFyJMc2q3digbRlJdAr8rZljTcwD1LsTL5coe76XOgSZiyj49Y2T+9bvWkPhu+rKH2rl2Knnv3QEFvAoemvo2282/icESOtq3wmBhGb+BpzZKYrGelSc675myeSTpf2XG4/G5BUH76xegKrV+fGqvWkcADqKch9+Ow83uzuGt031waWgwzEseYkCOCpIJLnJtNI2ytdv+EZ8JXhGTBy2BQ==[/tex]'], 'type': 102}

设向量[tex=0.714x1.214]Bon++APCFFqGDVhoG+r8OcUvNkjBYf5Cq6q6k0lSCE0=[/tex]可由向量组[tex=4.286x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrWhfdN8VXI6DbC98ejmhFVs=[/tex]线性表示，但不能由向量组[tex=2.714x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNtLDWYZJFoJfJul/K/b6eLQ==[/tex]线性表示.。记向量组[tex=2.714x1.0]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNtLDWYZJFoJfJul/K/b6eLQ==[/tex]为 ( I ) , 向量组[tex=3.786x1.214]spsZ+rMIOMiqBxP/ZoH2FwZfpjpMa8yyishLmJ54xHG8AZTASVlkJ08hVkWA2NiNBIazwKyqAvuKuneN4z3DrQcZK9XfefuS3QDVOGKqqRQ=[/tex]为 ( II ) , 则 未知类型：{'options': ['[tex=1.143x1.0]spsZ+rMIOMiqBxP/ZoH2F1eL4n6q3iQGmC3qijiKWqo=[/tex]不能由( I )线性表示，也不能由( II )线性表示', '[tex=1.143x1.0]spsZ+rMIOMiqBxP/ZoH2F1eL4n6q3iQGmC3qijiKWqo=[/tex]不能由( I )线性表示，但可由( II )线性表示', '[tex=1.143x1.0]spsZ+rMIOMiqBxP/ZoH2F1eL4n6q3iQGmC3qijiKWqo=[/tex]可由( I )线性表示，也可由( II )线性表示', '[tex=1.143x1.0]spsZ+rMIOMiqBxP/ZoH2F1eL4n6q3iQGmC3qijiKWqo=[/tex]可由( I )线性表示，但不可由( II )线性表示'], 'type': 102}

利用施密特正交化方法，把向量组[tex=6.571x1.5]spsZ+rMIOMiqBxP/ZoH2F5pmgmRcr8NdJc2GP6zS3yzzKHOqylFMCj9axZ43JQYl[/tex]，[tex=8.143x1.5]spsZ+rMIOMiqBxP/ZoH2F/jSaUEtfXUwSEYZFp9kjn5JDN5/PbM91EVL3ibkldKyVC4RfWkRz33WyJ8mMSshSg==[/tex]化为正交单位向量组．

设非零向量 [tex=5.929x1.714]Bon++APCFFqGDVhoG+r8OcZvX6w0c9EoTH8FI5fn971gncmvVPx31d+PsGRQ+VXwkElaG1yEx/hJqaK1gONiFA==[/tex] 能由 [tex=15.429x1.5]spsZ+rMIOMiqBxP/ZoH2F7wcTzs2AMZXazz7NYlWjwAb0Nx0b7ivJsIOxtX/0Jc5YRe+7BRShpxbwmVHctrUAQopqHFefKuZNM4hm1vSKcBxSclgGe9jUZt4+u1kPwfqnfOxiPY+wIWqjXDXQxS2Jg==[/tex][tex=7.357x1.5]spsZ+rMIOMiqBxP/ZoH2F6LjFV9xZBf5sPJXcgCSTgU9e6gJqmocq/S8CnJ92saRQ5/xKtjLkWtWPk+0Pu0T9g==[/tex]唯一线性表示,则 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 应取哪些值?

判定下列向量组是线性相关还是线性无关.[tex=18.5x1.357]spsZ+rMIOMiqBxP/ZoH2F5i6IrTwXNFp45WyNxPVsattR/I4uktA2LoQ3TQinwCaFA9XWcpBE7hs0h/vTgdYFSEr7eOBwFQ1A5rsgDeOlXwJWtHIZa5dmaKRibsPkjtrtiVO7UyTbPgsjP0Gl0frWA==[/tex]

在[tex=1.143x1.214]eAQo6GdrWeIAllUf5EVrqJy2ynf9dzuN0QK+rzoUrJo=[/tex]中求出与[tex=5.5x1.357]spsZ+rMIOMiqBxP/ZoH2F9Gz2yBAsbSctxvgXwuzqHI=[/tex]正交的向量组.

用施密特正交化方法把下列向量组标准正交化:[tex=17.929x3.643]spsZ+rMIOMiqBxP/ZoH2F2y3Q9X18LN9v4wmuMzCffS5Vc0ofl9qvMHeezXiONkXB8nGLbFqXHhVZak8iXxxZChLw4asPdgjSjllPT8bSE1NVt/HB7Khbng8B6yoyp+kDTtzvRtHzm3dZQJm62QIpN5rqI332i+GmzCtwKHWLrLgiYda3djnXrzzSzRGfF2fvru0CetA9F1QgEkChVIwuSu4fA5OpIc2ySAe2mEi3+Vhuo5EdPRIYaAUgX5fryFhvfqR+GKvKTUxwy/g7AfoAAlKQWjfQOrolspQ5pPz7ylP6U8jAEiBWhVBUouxYufV[/tex]