中央電大土木工程本科工程數(shù)學(xué)形成性考核冊答案

1、1工程數(shù)學(xué)作業(yè)（一）答案（滿分100分）第2章矩陣（一）單項(xiàng)選擇題（每小題2分，共20分）⒈設(shè)，則（D）aaabbbccc1231231232?aaaabababccc123112233123232323????A.4B.－4C.6D.－6⒉若，則（A）000100002001001aa?a?A.B.－1C.D.112?12⒊乘積矩陣中元素（C）1124103521??????????????c23?A.1B.7C.10D.8⒋設(shè)均為階

2、可逆矩陣，則下列運(yùn)算關(guān)系正確的是（B）ABnA.B.ABAB??????111()ABBA???11C.D.()ABAB??????111()ABAB????111⒌設(shè)均為階方陣，且，則下列等式正確的是（D）ABnk?0k?1A.B.ABAB???ABnAB?C.D.kAkA????kAkAn()⒍下列結(jié)論正確的是（A）A.若是正交矩陣，則也是正交矩陣AA?1B.若均為階對稱矩陣，則也是對稱矩陣ABnABC.若均為階非零矩陣，則也是非零

3、矩陣ABnABD.若均為階非零矩陣，則ABnAB?0⒎矩陣的伴隨矩陣為（C）1325??????A.B.1325????????????????1325C.D.5321????????????????5321⒏方陣可逆的充分必要條件是（B）AA.B.C.D.A?0A?0A?0A?0⒐設(shè)均為階可逆矩陣，則（D）ABCn()ACB???1A.B.()????BAC111???BCA11C.D.ACB????111()()BCA????111

4、⒑設(shè)均為階可逆矩陣，則下列等式成立的是（A）ABCnA.B.()ABAABB????2222()ABBBAB???2C.D.()221111ABCCBA?????()22ABCCBA?????3???????????????????????????????????252112712511234511725223821)3(21BAX⒋寫出4階行列式1020143602533110??中元素的代數(shù)余子式，并求其值aa4142答案答案：03

5、52634020)1(1441?????a45350631021)1(2442??????a⒌用初等行變換求下列矩陣的逆矩陣：⑴；⑵；⑶122212221????????????1234231211111026???????????????1000110011101111????????????解：（1）???????????????????????????????????????????????????????????????????

6、?????????????????????????????????????????????????????919292929192929291100010001919292031320323110021020112201203231900630201102012001360630221100010001122212221|2313323212312122913123222rrrrrrrrrrrrrrIA?????????????????