自考 线性代数郭文军 串讲班 线性代数习题解答.ppt.pdfVIP免费

线性代数习题解习题一A组1.计算下列二阶行列式（1）521-12（2）012896（3）2222baabbaba（4）11112322xxxxxx2.计算下列三阶行列式（1）132213321=1+8+27-6-6-6=18（2）5598413111（3）7140053101（4）000000dcba3.当k取何值时，100143kkk=0.解：100143kkk0)3(0)(02kk，得0342kk，所以1k或3k。4.求下列排列的逆序数.解：(1)512110)51324(.(2)8142010)426315(.(3)21123456)7654321(.(4)1340423000)36715284(.5.下列各元素乘积是否是五阶行列式ija中一项?如果是,该项应取什么符号?解：(2)不是.因为5145332211aaaaa中有俩个元素在第一列.(3)是.对应项为534531241224513)1(aaaaa）（1021)24153(所以该项应取负号。6.选择i,j使jiaaaaa54234213成为五阶行列式ija中带有负号的项解:当)5,1(),(ji时,30102)31425(,是奇排列.当)1,5(),(ji时,81232)35421(,是偶排列.所以i=1,j=5.8.利用行列式性质计算下列行列式.解:(1)11121232123043032123121rrrr620043032132rr(2)6217213424435431014327427246621721100044354320003274271000123ccc621721144354323274271103.62110014431002327100110323cc62111443123271110531212rrrr294002111032711105=294105(3)1111111111111111820000200002011114,3,21irri(4)15023213531404221502321353140211211203840553002112234413121rrrrrr11205100046100211223424rrrr7130051000461002112242rr71300120046100211)5(202700120046100211)5(2743rr270002100641020111043cc270.（5）yyxx1111111111111111yyyxxxcccc11011010110123412yyxxrrrr00011000010124321yyxx000110001010122320001000010101yxyyxxrr（6）dcbacbabaadcbacbabaadcbacbabaadcba3610363234232cbabaacbabaacbabaadcbairri36103630234232004,3,21baabaacbabaadcbarrrr37300200032423244300020003aabaacbabaadcbarr9.用行列式性质证明:(1)3...