2017经济数学基础小抄3-2（线性代数完整版电大小抄）-2017电大专科考试小抄（2017已更新）

经济数学基础线性代数一、单项选择题1设A为23矩阵，B为3矩阵，则下列运算中（A）可以进行AABBABTCABDBAT2设,为同阶可逆矩阵，则下列等式成立的是（B）ABTABC11D113设,为同阶可逆方阵，则下列说法正确的是（D）A若ABI，则必有AI或BIBTC秩秩秩D114设,均为N阶方阵，在下列情况下能推出A是单位矩阵的是（D）ABCIDI5设是可逆矩阵，且，则（C）ABCD6设21，31，I是单位矩阵，则IBT（D）A3B6C52D537设下面矩阵A,B,C能进行乘法运算，那么（B）成立AABAC，A0，则BCBABAC，A可逆，则BCCA可逆，则ABBADAB0，则有A0，或B08设是阶可逆矩阵，是不为0的常数，则（C）ABCD9设3142，则RA（D）A4B3C2D110设线性方程组BX的增广矩阵通过初等行变换化为0012436，则此线性方程组的一般解中自由未知量的个数为（A）A1B2C3D411线性方程组011X解的情况是（A）A无解B只有0解C有唯一解D有无穷多解12若线性方程组的增广矩阵为12，则当（A）时线性方程组无解A12B0C1D213线性方程组只有零解，则（B）A有唯一解B可能无解C有无穷多解D无解14设线性方程组AXB中，若RA,B4，RA3，则该线性方程组（B）A有唯一解B无解C有非零解D有无穷多解15设线性方程组X有唯一解，则相应的齐次方程组OX（C）A无解B有非零解C只有零解D解不能确定16设A为23矩阵，B为矩阵，则下列运算中（A）可以进行AABBABTCABDBAT17设,为同阶可逆矩阵，则下列等式成立的是（B）ABAC11DT11B18设,为同阶可逆方阵，则下列说法正确的是（D）A若ABI，则必有AI或BIBTC秩秩秩D1119设,均为N阶方阵，在下列情况下能推出A是单位矩阵的是（D）ABCIDI20设是可逆矩阵，且，则（C）ABCD21设21，31，I是单位矩阵，则IBT（D）A63B62C52D5322设下面矩阵A,B,C能进行乘法运算，那么（B）成立AABAC，A0，则BCBABAC，A可逆，则BCCA可逆，则ABBADAB0，则有A0，或B023若线性方程组的增广矩阵为412，则当（D）时线性方程组有无穷多解A1B1C2D24若非齐次线性方程组AMNXB的C，那么该方程组无解A秩ANB秩AMC秩A）秩D秩A）秩25线性方程组021X解的情况是（A）A无解B只有0解C有唯一解D有无穷多解26线性方程组只有零解，则（B）A有唯一解B可能无解C有无穷多解D无解27设线性方程组AXB中，若RA,B4，RA3，则该线性方程组（B）A有唯一解B无解C有非零解D有无穷多解28设线性方程组X有唯一解，则相应的齐次方程组OX（C）A无解B有非零解C只有零解D解不能确定30设A,B均为同阶可逆矩阵,则下列等式成立的是BAABTATBTBABTBTATCABT1A1BT1DABT1A1B1T解析AB1B1A1ABTBTAT故答案是B31设A12,B13,E是单位矩阵,则ATBEAA523B62C623D52解析ATBE3101011）（）（32设线性方程组AXB的增广矩阵为84021315,则此线性方程组一般解中自由未知量的个数为AA1B2C3D4解析001234158402153233若线性方程组的增广矩阵为A,B2,则当D时线性方程组有无穷多解A1B4C2D1解析D201222时有无穷多解，选故34线性方程组021X解的情况是AA无解B只有零解C有惟一解D有无穷多解解析1AR2B,R01BA选故，35以下结论或等式正确的是（C）A若B,均为零矩阵，则有AB若，且O，则CC对角矩阵是对称矩阵D若,，则36设为43矩阵，为25矩阵，且乘积矩阵TB有意义，则T为（A）矩阵A2BC53D337设BA,均为N阶可逆矩阵，则下列等式成立的是（C）A11，B11BACBAD38下列矩阵可逆的是（A）A302B3210C01D2139矩阵4的秩是（B）A0B1C2D3二、填空题1两个矩阵,既可相加又可相乘的充分必要条件是A与B是同阶矩阵2计算矩阵乘积1023243若矩阵A1，B，则ATB264134设为矩阵，为矩阵，若AB与BA都可进行运算，则有关系式5设1320A，当0时，是对称矩阵6当时，矩阵AA3可逆7设B,为两个已知矩阵，且BI可逆，则方程XA的解ABI18设为N阶可逆矩阵，则RAN9若矩阵A30241，则RA210若RA,B4，RA3，则线性方程组AXB无解11若线性方程组21X有非零解，则112设齐次线性方程组0NMX，且秩ARN，则其一般解中的自由未知量的个数等于NR13齐次线性方程组A的系数矩阵为0213则此方程组的一般解为4231X其中43,X是自由未知量14线性方程组的增广矩阵化成阶梯形矩阵后为10021DA则当1时，方程组有无穷多解15若线性方程组有唯一解，则只有0解16两个矩阵B,既可相加又可相乘的充分必要条件是答案同阶矩阵17若矩阵A21，B1，则ATB答案24118设30A，当时，是对称矩阵答案0A19当时，矩阵AA13可逆答案320设B,为两个已知矩阵，且BI可逆，则方程XA的解答案ABI121设A为N阶可逆矩阵，则RA答案N22若矩阵A30241，则RA答案223若RA,B4，RA3，则线性方程组AXB答案无解24若线性方程组21X有非零解，则答案125设齐次线性方程组01NMX，且秩ARN，则其一般解中的自由未知量的个数等于答案RN26齐次线性方程组A的系数矩阵为0213则此方程组的一般解为答案4231X其中43,X是自由未知量27线性方程组的增广矩阵化成阶梯形矩阵后为10021DA则当时，方程组有无穷多解答案D28计算矩阵乘积10321429设A为N阶可逆矩阵,则RAN30设矩阵A34,E为单位矩阵,则EAT24031若线性方程组021X有非零解,则132若线性方程组AXBBO有惟一解,则AXO无非零解33设矩阵162235401A，则A的元素_23A答案334设B,均为3阶矩阵，且B，则T答案7235设均为N阶矩阵，则等式22B成立的充分必要条件是答案A36设,均为阶矩阵，I可逆，则矩阵XA的解_答案I137设矩阵302A，则_1答案3102三、计算题1设矩阵1342A，3012B，求BAIT1解因为TI142204314203所以BAIT1031052设矩阵021A，201B，2416C，计算CBAT2解CBT2046416203设矩阵A123，求1A3解因为AI10461022743271077210103所以A1210734设矩阵A4，求逆矩阵1A4解因为AI120830140124134123410所以A123425设矩阵A01，B1436，计算AB15解因为AB22ABI1014220所以AB116设矩阵A021，B213，计算BA16解因为BA10245BAI114355202503所以BA1317解矩阵方程242X7解因为1031043223即34321所以，X8解矩阵方程0215318解因为1301325即132521所以，X01325040389设线性方程组BAXX321讨论当A，B为何值时，方程组无解，有唯一解，有无穷多解9解因为4210120BABA30所以当1A且3B时，方程组无解；当时，方程组有唯一解；当且时，方程组有无穷多解10设线性方程组05223112X，求其系数矩阵和增广矩阵的秩，并判断其解的情况10解因为21051223A3012所以RA2，R3又因为RAR，所以方程组无解11求下列线性方程组的一般解03522412XX11解因为系数矩阵1035120A012所以一般解为432X（其中3，4X是自由未知量）12求下列线性方程组的一般解1264235321XX12解因为增广矩阵180912642315A00194所以一般解为19321X（其中3是自由未知量）13设齐次线性方程组08352312XX问取何值时方程组有非零解，并求一般解13解因为系数矩阵A610283521501所以当5时，方程组有非零解且一般解为321X（其中3是自由未知量）14当取何值时，线性方程组1542312X有解并求一般解14解因为增广矩阵261050142A26所以当0时，线性方程组有无穷多解，且一般解为2615321XX3是自由未知量15已知线性方程组BAX的增广矩阵经初等行变换化为300116A问取何值时，方程组BX有解当方程组有解时，求方程组BAX的一般解15解当3时，2R，方程组有解当3时，00310316A一般解为4321XX，其中3,4为自由未知量16设矩阵A0，B21，计算BA1解因为BA2130435BAI10245520115317设矩阵8437A，是3阶单位矩阵，求1AI解由矩阵减法运算得9437284321001I利用初等行变换得即18设矩阵12,3210BA，求A1解利用初等行变换得1023401032146514601135即46A由矩阵乘法得7641246351B19求解线性方程组的一般解023421XX解将方程组的系数矩阵化为阶梯形0130231310231108一般解为038421XX是自由未知量20求当取何值时，线性方程X有解，在有解的情况下求方程组的一般解解将方程组的增广矩阵化为阶梯形10051219020512147963122所以，当时，方程组有解，且有无穷多解，00589答案43215098XX其中43,是自由未知量21求当取何值时，线性方程组4321172XX解将方程组的增广矩阵化为阶梯形273501471200352当时，方程组有解，且方程组的一般解为43215764XX其中43,为自由未知量22计算7230165211解7230165474012941431420523设矩阵1023B1032，A，求AB。解因为B2101231032322B所以0A（注意因为符号输入方面的原因，在题4题7的矩阵初等行变换中，书写时应把（1）写成；（2）写成；（3）写成；）24设矩阵012，确定的值，使AR最小。解43,2104213740147230491当时，2AR达到最小值。25求矩阵32140758的秩。解32140758A3,13214580741235361527093,200197AR。26求下列矩阵的逆矩阵（1）103解AI02132103407922310402114239431022132943178532172A（2）A12436解I102321012430134262043,234206232103132107A1210727设矩阵3,53B，求解矩阵方程BXA解AI1012130021231021532BAX10四、证明题1试证设A，B，AB均为N阶对称矩阵，则ABBA1证因为ATA，BTB，ABTAB所以ABABTBTATBA2试证设是N阶矩阵，若30，则21AII2证因为2I3所以13已知矩阵2IBA，且A2，试证B是可逆矩阵，并求13证因为4I，且A2，即21I，得IB2，所以是可逆矩阵，且B4设阶矩阵满足，TA，证明是对称矩阵4证因为ITIA所以是对称矩阵5设A，B均为N阶对称矩阵，则ABBA也是对称矩阵5证因为BTT，且TTBA所以ABBA是对称矩阵6、试证若21,B都与可交换，则21，1也与A可交换。证，2B211B即21也与A可交换。212即B也与可交换7试证对于任意方阵，T，AT,是对称矩阵。证TTTAAAT是对称矩阵。是对称矩阵。TTTA是对称矩阵8设B,均为N阶对称矩阵，则AB对称的充分必要条件是BA。证必要性T，T若是对称矩阵，即而A因此充分性若B，则ABTT是对称矩阵9设为N阶对称矩阵，为N阶可逆矩阵，且T1，证明1是对称矩阵。证ATT11B是对称矩阵证毕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