1、完整版高等代数北大版第8章习题参考答案doc第八章 矩阵1.化下列矩阵成标准形3221)2532003)0000(1) 23223215) 42353224222122)1222000200204)0(1)2002000233 4123014360226)0620101003312200解 1)对矩阵作初等变换 , 有A ()32 23252532 230= B () ,0310 23B ( ) 即为所求。2)对矩阵作初等变换 , 有1212A ()0122212210000= B () ,00223 50 3 - 10 2 - 3100000( 1)B ( ) 即为所求。2003)因为00的
2、行列式因子为00(1) 2D 1 =1,D 2 =(1) ,D 3 =2 (1)3 ,所以d 1 = 1,d 2 = D 2 =(1) ,d 3 = D 3 =(1) 2 ,D 1D 2从而200100A ( )000(1)0= B ( ) ,00(1) 200(1) 2B () 即为所求。00020020 的行列式因子为4)因为1) 200(02000D 1 =1,D 2= (1) ,D 3=2 (1) 2 ,D 4=4 (1) 4 ,所以d 1 = 1, d 2 = D 2 =(1) , d 3 = D 3 = (1) , d 4 = D 4 =2 ( 1) 2 ,D1D 2D 3从而00
3、020020A ()0(1) 200200010020(1)00= B () ,00(- 1)00002 (-1)2B () 即为所求。5)对 矩阵作初等变换 , 有A ( )B ( ) 即为所求。32232122342353223424213222122423322222214726322450211000132132245001000132100010001100010= B () ,003216)对矩阵作初等变换, 有2301436022A ( )06201010033122000001000220020101000100000010000002010000010000001000020000100000100000010000020000100000100010000020000000,0001000001在最后一个行列式中D 3 =1,D 4 =(1) ,D 5 =3 (1)2 ,所以d 1=d 2= d 3 =1,d 4=D 4= (1),d 5 =D 5 =2 (1) 。D 3D 4故所求标准形为1000001000B ()=00100。000(1)000002 (1)2. 求下列矩阵的不变因子 :2101000101)0212)01002054321000103)01012004)20001002000100002005)010