简答题:设向量组<img src="http://www.weimei168.com/uploads/202208/161258475586051.png" width="70" height="30" />线性无关，β<img src="http://www.weimei168.com/uploads/202208/161258476015271.png" width="10" height="29" />=<img src="http://www.weimei168.com/uploads/202208/161258476655601.png" width="24" height="29" />-<img src="http://www.weimei168.com/uploads/202208/161258477290541.png" width="22" height="30" />，β<img src="http://www.weimei168.com/uploads/202208/161258477858351.png" width="14" height="29" />=<img src="http://www.weimei168.com/uploads/202208/161258478319391.png" width="20" height="29" />-<img src="http://www.weimei168.com/uploads/202208/161258476655601.png" width="24" height="29" />+2<img src="http://www.weimei168.com/uploads/202208/161258477290541.png" width="22" height="30" />，β<img src="http://www.weimei168.com/uploads/202208/161258484236861.png" width="12" height="30" />=2<img src="http://www.weimei168.com/uploads/202208/161258478319391.png" width="20" height="29" />-<img src="http://www.weimei168.com/uploads/202208/161258476655601.png" width="24" height="29" />+3<img src="http://www.weimei168.com/uploads/202208/161258477290541.png" width="22" height="30" />，证明：β<img src="http://www.weimei168.com/uploads/202208/161258476015271.png" width="10" height="29" />，β<img src="http://www.weimei168.com/uploads/202208/161258477858351.png" width="14" height="29" />，β<img src="http://www.weimei168.com/uploads/202208/161258484236861.png" width="12" height="30" />是线性相关的．