【单选题】【消耗次数：1】
以下结论中不正确的是（）
①
若存在可逆矩阵<imgwidth="18"height="20"v:shapes="_x0000_i1238"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image243.png">，使<imgwidth="70"height="24"v:shapes="_x0000_i1239"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image245.png">，则<imgwidth="18"height="18"v:shapes="_x0000_i1240"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image246.png">是正定矩阵
②
二次型<imgwidth="158"height="28"v:shapes="_x0000_i1241"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image248.png">是正定二次型
③
<imgwidth="14"height="16"v:shapes="_x0000_i1242"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image249.png">元实二次型正定的充分必要条件是<imgwidth="18"height="24"v:shapes="_x0000_i1243"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image233.png">的正惯性指数为<imgwidth="14"height="16"v:shapes="_x0000_i1244"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image249.png">
④
<imgwidth="14"height="16"v:shapes="_x0000_i1245"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image249.png">阶实对称矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1246"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image246.png">正定的充分必要条件是<imgwidth="18"height="18"v:shapes="_x0000_i1247"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image246.png">的特征值全为正数
参考答案：
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相关题目
【单选题】
若<imgwidth="14"height="16"v:shapes="_x0000_i1178"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image188.png">阶可逆矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1179"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">与<imgwidth="18"height="18"v:shapes="_x0000_i1180"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">相似，且<imgwidth="56"height="22"v:shapes="_x0000_i1181"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image192.png">则<imgwidth="40"height="22"v:shapes="_x0000_i1182"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image194.png">（）
①
<imgwidth="30"height="18"v:shapes="_x0000_i1183"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image196.png">
②
<imgwidth="28"height="18"v:shapes="_x0000_i1184"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image198.png">
③
<imgwidth="18"height="18"v:shapes="_x0000_i1185"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">
④
<imgwidth="26"height="22"v:shapes="_x0000_i1186"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image201.png">
【单选题】
<imgwidth="18"height="18"v:shapes="_x0000_i1269"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image290.png">为同阶方阵，<imgwidth="66"height="114"v:shapes="_x0000_i1270"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image292.png">且<imgwidth="100"height="24"v:shapes="_x0000_i1271"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image294.png">，当（）时，<imgwidth="48"height="18"v:shapes="_x0000_i1272"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image296.png">
①
<imgwidth="90"height="24"v:shapes="_x0000_i1273"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image298.png">
②
<imgwidth="58"height="22"v:shapes="_x0000_i1274"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image300.png">
③
<imgwidth="58"height="22"v:shapes="_x0000_i1275"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image302.png">
④
<imgwidth="58"height="22"v:shapes="_x0000_i1276"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image300.png">且<imgwidth="58"height="22"v:shapes="_x0000_i1277"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image302.png">
【单选题】
设<imgwidth="18"height="18"v:shapes="_x0000_i1203"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1204"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">是<imgwidth="14"height="16"v:shapes="_x0000_i1205"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image188.png">阶矩阵，则下列命题成立的是（）
①
<imgwidth="18"height="18"v:shapes="_x0000_i1206"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1207"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">等价则<imgwidth="18"height="18"v:shapes="_x0000_i1208"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1209"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">相似
②
<imgwidth="18"height="18"v:shapes="_x0000_i1210"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1211"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">相似则<imgwidth="18"height="18"v:shapes="_x0000_i1212"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1213"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">等价
③
<imgwidth="18"height="18"v:shapes="_x0000_i1214"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1215"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">等价则<imgwidth="18"height="18"v:shapes="_x0000_i1216"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1217"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">合同
④
<imgwidth="18"height="18"v:shapes="_x0000_i1218"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1219"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">相似则<imgwidth="18"height="18"v:shapes="_x0000_i1220"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image189.png">和<imgwidth="18"height="18"v:shapes="_x0000_i1221"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image190.png">合同
【单选题】
设三阶方阵<imgwidth="18"height="18"v:shapes="_x0000_i1085"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的特征值为<imgwidth="52"height="22"v:shapes="_x0000_i1086"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image064.png">，对应的特征向量为<imgwidth="70"height="26"v:shapes="_x0000_i1087"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image066.png">，若<imgwidth="32"height="18"v:shapes="_x0000_i1088"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image068.png"><imgwidth="84"height="26"v:shapes="_x0000_i1089"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image070.png">，则<imgwidth="68"height="22"v:shapes="_x0000_i1090"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image072.png">
①
<imgwidth="82"height="84"v:shapes="_x0000_i1091"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image074.png">
②
<imgwidth="82"height="84"v:shapes="_x0000_i1092"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image076.png">
③
<imgwidth="94"height="84"v:shapes="_x0000_i1093"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image078.png">
④
<imgwidth="94"height="84"v:shapes="_x0000_i1094"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image080.png">
【单选题】
若方阵<imgwidth="18"height="18"v:shapes="_x0000_i1064"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">与<imgwidth="18"height="18"v:shapes="_x0000_i1065"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image032.png">等价，则（）
①
<imgwidth="86"height="22"v:shapes="_x0000_i1066"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image034.png">
②
<imgwidth="202"height="24"v:shapes="_x0000_i1067"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image036.png">
③
<imgwidth="118"height="24"v:shapes="_x0000_i1068"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image038.png">
④
存在可逆矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1069"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image040.png">，使<imgwidth="84"height="22"v:shapes="_x0000_i1070"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image042.png">
【单选题】
设<imgwidth="16"height="20"v:shapes="_x0000_i1143"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image129.png">是可逆矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1144"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image091.png">的一个特征值，则<imgwidth="18"height="18"v:shapes="_x0000_i1145"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image091.png">的伴随矩阵<imgwidth="22"height="22"v:shapes="_x0000_i1146"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image131.png">必有一个特征值为（）
①
<imgwidth="78"height="48"v:shapes="_x0000_i1147"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image133.png">
②
<imgwidth="58"height="48"v:shapes="_x0000_i1148"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image135.png">
③
<imgwidth="56"height="20"v:shapes="_x0000_i1149"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image137.png">
④
<imgwidth="74"height="32"v:shapes="_x0000_i1150"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image139.png">
【单选题】
设<imgwidth="18"height="18"v:shapes="_x0000_i1095"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">是一个<imgwidth="14"height="16"v:shapes="_x0000_i1096"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image002.png">阶<imgwidth="40"height="20"v:shapes="_x0000_i1097"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image082.png">阶方阵，下列陈述中正确的是（）
①
如存在数<imgwidth="16"height="20"v:shapes="_x0000_i1098"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image010.png">和向量<imgwidth="18"height="16"v:shapes="_x0000_i1099"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image084.png">使<imgwidth="72"height="20"v:shapes="_x0000_i1100"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image086.png">，则<imgwidth="18"height="16"v:shapes="_x0000_i1101"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image084.png">是<imgwidth="18"height="18"v:shapes="_x0000_i1102"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的属于特征值<imgwidth="16"height="20"v:shapes="_x0000_i1103"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image010.png">的特征向量
②
如存在数<imgwidth="16"height="20"v:shapes="_x0000_i1104"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image010.png">和非零向量<imgwidth="18"height="16"v:shapes="_x0000_i1105"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image084.png">，使<imgwidth="114"height="28"v:shapes="_x0000_i1106"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image088.png">，则<imgwidth="16"height="20"v:shapes="_x0000_i1107"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image010.png">是<imgwidth="18"height="18"v:shapes="_x0000_i1108"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的特征值
③
<imgwidth="18"height="18"v:shapes="_x0000_i1109"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的2个不同的特征值可以有同一个特征向量
④
<imgwidth="64"height="26"v:shapes="_x0000_i1110"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image090.png">是<imgwidth="18"height="18"v:shapes="_x0000_i1111"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的3个互不相同的特征值，<imgwidth="70"height="26"v:shapes="_x0000_i1112"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image066.png">依次是<imgwidth="18"height="18"v:shapes="_x0000_i1113"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的属于<imgwidth="64"height="26"v:shapes="_x0000_i1114"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image090.png">的特征向量，则<imgwidth="70"height="26"v:shapes="_x0000_i1115"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image066.png">有可能线性相关
【单选题】
已知<imgwidth="18"height="18"v:shapes="_x0000_i1035"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">为<imgwidth="14"height="16"v:shapes="_x0000_i1036"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image002.png">阶方阵，以下说法错误的是（）
①
<imgwidth="150"height="34"v:shapes="_x0000_i1037"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image006.png">
②
<imgwidth="18"height="18"v:shapes="_x0000_i1038"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的全部特征向量为<imgwidth="118"height="28"v:shapes="_x0000_i1039"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image008.png">的全部解
③
若<imgwidth="18"height="18"v:shapes="_x0000_i1040"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">有<imgwidth="14"height="16"v:shapes="_x0000_i1041"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image002.png">个互不相同的特征值，则必有<imgwidth="14"height="16"v:shapes="_x0000_i1042"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image002.png">个线性无关的特征向量
④
若<imgwidth="18"height="18"v:shapes="_x0000_i1043"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">可逆，而矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1044"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image004.png">的属于特征值<imgwidth="16"height="20"v:shapes="_x0000_i1045"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image010.png">的特征向量也是矩阵<imgwidth="28"height="22"v:shapes="_x0000_i1046"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image012.png">属于特征值<imgwidth="19"height="42"v:shapes="_x0000_i1047"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image014.png">的特征向量
【单选题】
已知<imgwidth="34"height="22"v:shapes="_x0000_i1231"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image291.png">均为<imgwidth="14"height="16"v:shapes="_x0000_i1232"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image293.png">阶方阵且<imgwidth="18"height="18"v:shapes="_x0000_i1233"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image285.png">与<imgwidth="18"height="18"v:shapes="_x0000_i1234"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image295.png">相似，若<imgwidth="56"height="22"v:shapes="_x0000_i1235"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image297.png">，则<imgwidth="24"height="22"v:shapes="_x0000_i1236"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image299.png">为（）
①
<imgwidth="24"height="22"v:shapes="_x0000_i1237"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image301.png">
②
<imgwidth="18"height="18"v:shapes="_x0000_i1238"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image285.png">
③
<imgwidth="18"height="18"v:shapes="_x0000_i1239"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image303.png">
④
<imgwidth="54"height="22"v:shapes="_x0000_i1240"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image305.png">
【单选题】
已知方阵<imgwidth="126"height="84"v:shapes="_x0000_i1154"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image145.png">相似于对角阵，则常数<imgwidth="30"height="16"v:shapes="_x0000_i1155"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image147.png">（）
①
<imgwidth="14"height="20"v:shapes="_x0000_i1156"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image149.png">
②
<imgwidth="10"height="18"v:shapes="_x0000_i1157"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image151.png">
③
<imgwidth="14"height="18"v:shapes="_x0000_i1158"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image153.png">
④
<imgwidth="24"height="18"v:shapes="_x0000_i1159"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds05.files/image155.png">
【单选题】
<imgwidth="14"height="16"v:shapes="_x0000_i1205"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image137.png">阶方阵<imgwidth="18"height="18"v:shapes="_x0000_i1206"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image251.png">与<imgwidth="18"height="18"v:shapes="_x0000_i1207"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image253.png">相似的充分必要条件是（）
①
<imgwidth="86"height="22"v:shapes="_x0000_i1208"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image255.png">
②
存在可逆矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1209"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image257.png">与<imgwidth="18"height="24"v:shapes="_x0000_i1210"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image259.png">使得<imgwidth="74"height="24"v:shapes="_x0000_i1211"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image261.png">
③
存在可逆矩阵<imgwidth="16"height="18"v:shapes="_x0000_i1212"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image263.png">使得<imgwidth="82"height="22"v:shapes="_x0000_i1213"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image265.png">
④
存在可逆矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1214"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image257.png">使得<imgwidth="84"height="22"v:shapes="_x0000_i1215"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image268.png">
随机题目