文档介绍：09级《线性代数》()阶段练习题(二)A一、填空题11?3?1????A?3?1?34,.?A)R(????89?15???11?3?111?3?111?3?1????????????::.2)?R(3A??1?34A4?6?70?467,0:解????????????0004?615?9?8?700??????12?2????3,BA?,且,???????113???212?A?4t??3t213?7t??0,?因此,.解:定非可逆阵A31?1*)?A0R(.()2,?(A)RA????????????,?k,??,?,,,????????????,?2?2,?k??,,k?线性相关时,.,则当2?k4**********解:1000????k1k2????????????????????K?,,,,,,,,,?,4**********??2?0k1??1011??????,,,,则K43211000k2kk1k2?0k?2?2(k?2)??K0,?k??11111101?????????,2?3,2??,,线性线性无关,.:?????????????)2,1,,()?2??3(,0?2??331223213??332??100??????,210?1?0K?为非奇矩阵,故向量组而,,?22?3?K332123321线性无关.?????????????,?,?,,,?,向量组线性无关,**********:1001????1100??????????????????,?,???,?,,,,434223114213??0110??0011??10100100110011K??110?011?1?1?0,故向量组其中01100110010011?????????,???,,????,t,)??(1,1,0)(2,,5,?(2,0,1)?t?31232??,????????,,,,线线性相关时解:只有当向量组可由线性无关,?????0,t?5?2t?,,5?10??3????????2x?4x?6x?03?2?????431???,?.线性方程组的基础解系为8.?12????103x?6x?9x?0?234????01????对方程组的系数阵进行初等变换解:20?4610?23????:????036?9012?3????x?2x?3xx10???????4133取和同解,令,可得方程组的基础解原方程组与???????xx??2x?3x10???????4432TT??????.读11200,3?3??2?21???,,,?A)R(b?Ax32125?????????08????TT????,4)8,?(5,3,?(2,0,2),28,?3bAx?321????37?????26?????解:,存在基础解系(只有一个线性无关的解向量).0A)?