【单选题】【消耗次数：1】
若存在一可逆阵<imgwidth="18"height="18"v:shapes="_x0000_i1303"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image388.png">使得<imgwidth="54"height="22"v:shapes="_x0000_i1304"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image390.png">为对角阵，其中<imgwidth="134"height="84"v:shapes="_x0000_i1305"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image392.png">，则<imgwidth="18"height="18"v:shapes="_x0000_i1306"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image388.png">为（）
①
<imgwidth="84"height="84"v:shapes="_x0000_i1307"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image394.png">
②
<imgwidth="84"height="84"v:shapes="_x0000_i1308"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image394.png">
③
<imgwidth="84"height="84"v:shapes="_x0000_i1309"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image396.png">
④
<imgwidth="84"height="84"v:shapes="_x0000_i1310"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image398.png">
参考答案：
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【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】
设<imgwidth="162"height="26"v:shapes="_x0000_i1348"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image448.png">是三阶方阵的三个特征值，对应特征向量分别为<imgwidth="62"height="26"v:shapes="_x0000_i1349"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image450.png">，且存在可逆矩阵<imgwidth="17"height="18"v:shapes="_x0000_i1350"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image452.png">，使得<imgwidth="54"height="22"v:shapes="_x0000_i1351"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image390.png"><imgwidth="118"height="84"v:shapes="_x0000_i1352"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image455.png">，则<imgwidth="32"height="18"v:shapes="_x0000_i1353"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image457.png">（）
①
<imgwidth="78"height="28"v:shapes="_x0000_i1354"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image459.png">
②
<imgwidth="78"height="28"v:shapes="_x0000_i1355"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image461.png">
③
<imgwidth="78"height="28"v:shapes="_x0000_i1356"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image463.png">
④
<imgwidth="78"height="28"v:shapes="_x0000_i1357"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image465.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">
【单选题】
<imgwidth="44"height="16"v:shapes="_x0000_i1068"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image062.png">矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1069"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的秩为<imgwidth="18"height="16"v:shapes="_x0000_i1070"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image065.png">，则（）
①
<imgwidth="18"height="18"v:shapes="_x0000_i1071"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的任意一个<imgwidth="18"height="16"v:shapes="_x0000_i1072"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image065.png">阶子式都不等于零
②
<imgwidth="18"height="18"v:shapes="_x0000_i1073"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的任意一个<imgwidth="42"height="20"v:shapes="_x0000_i1074"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image068.png">阶子式都不等于零
③
<imgwidth="18"height="18"v:shapes="_x0000_i1075"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的任意<imgwidth="18"height="16"v:shapes="_x0000_i1076"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image065.png">个列向量必线性无关
④
对于任一<imgwidth="18"height="16"v:shapes="_x0000_i1077"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image065.png">维列向量<imgwidth="14"height="20"v:shapes="_x0000_i1078"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image070.png">，矩阵<imgwidth="56"height="28"v:shapes="_x0000_i1079"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image072.png">的秩都为<imgwidth="18"height="16"v:shapes="_x0000_i1080"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image065.png">
【单选题】
设<imgwidth="48"height="26"v:shapes="_x0000_i1189"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image226.png">是<imgwidth="16"height="18"v:shapes="_x0000_i1190"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image220.png">的特征值且<imgwidth="54"height="22"v:shapes="_x0000_i1191"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image228.png">，则<imgwidth="26"height="28"v:shapes="_x0000_i1192"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image230.png">是（）特征值
①
<imgwidth="28"height="18"v:shapes="_x0000_i1193"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image232.png">
②
<imgwidth="26"height="22"v:shapes="_x0000_i1194"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image234.png">
③
<imgwidth="22"height="22"v:shapes="_x0000_i1195"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image236.png">
④
<imgwidth="28"height="22"v:shapes="_x0000_i1196"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image238.png">
【单选题】
若方阵<imgwidth="100"height="58"v:shapes="_x0000_i1264"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image337.png">，则<imgwidth="18"height="18"v:shapes="_x0000_i1265"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image285.png">的特征方程为（
①
<imgwidth="100"height="58"v:shapes="_x0000_i1266"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image339.png">
②
<imgwidth="112"height="24"v:shapes="_x0000_i1267"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image341.png">
③
<imgwidth="100"height="58"v:shapes="_x0000_i1268"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image343.png">
④
<imgwidth="112"height="24"v:shapes="_x0000_i1269"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image345.png">
【单选题】
若<imgwidth="56"height="22"v:shapes="_x0000_i1197"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image240.png">，则<imgwidth="16"height="18"v:shapes="_x0000_i1198"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image220.png">的特征值为（）
①
<imgwidth="22"height="18"v:shapes="_x0000_i1199"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image242.png">或<imgwidth="10"height="18"v:shapes="_x0000_i1200"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image244.png">
②
<imgwidth="14"height="20"v:shapes="_x0000_i1201"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image246.png">或<imgwidth="10"height="18"v:shapes="_x0000_i1202"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image244.png">
③
<imgwidth="14"height="20"v:shapes="_x0000_i1203"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image246.png">
④
<imgwidth="10"height="18"v:shapes="_x0000_i1204"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image244.png">
【单选题】
设<imgwidth="18"height="18"v:shapes="_x0000_i1034"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">为<imgwidth="14"height="16"v:shapes="_x0000_i1035"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image004.png">阶方阵，<imgwidth="18"height="18"v:shapes="_x0000_i1036"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image010.png">是<imgwidth="18"height="18"v:shapes="_x0000_i1037"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">经过若干次矩阵的初等变换后得到的矩阵，则有（）
①
<imgwidth="64"height="22"v:shapes="_x0000_i1038"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image012.png">
②
<imgwidth="66"height="22"v:shapes="_x0000_i1039"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image014.png">
③
若<imgwidth="54"height="22"v:shapes="_x0000_i1040"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image016.png">，则一定有<imgwidth="54"height="22"v:shapes="_x0000_i1041"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image018.png">
④
<imgwidth="54"height="22"v:shapes="_x0000_i1042"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image020.png">，则一定有<imgwidth="54"height="22"v:shapes="_x0000_i1043"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image022.png">
【单选题】
设<imgwidth="14"height="16"v:shapes="_x0000_i1089"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image004.png">元齐次线性方程组<imgwidth="54"height="20"v:shapes="_x0000_i1090"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image030.png">的通解为<imgwidth="108"height="32"v:shapes="_x0000_i1091"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image083.png">则矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1092"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的秩（）
①
<imgwidth="62"height="24"v:shapes="_x0000_i1093"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image086.png">
②
<imgwidth="90"height="24"v:shapes="_x0000_i1094"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image088.png">
③
<imgwidth="66"height="24"v:shapes="_x0000_i1095"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image079.png">
④
<imgwidth="18"height="18"v:shapes="_x0000_i1096"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image008.png">的每行元素之和都不等于零
【单选题】
<imgwidth="14"height="16"v:shapes="_x0000_i1251"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image293.png">阶实对称矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1252"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image285.png">的<imgwidth="14"height="16"v:shapes="_x0000_i1253"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image293.png">个行向量是一组正交单位向量组，则<imgwidth="18"height="18"v:shapes="_x0000_i1254"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image285.png">是（）
①
对称矩阵
②
正交矩阵
③
反对称矩阵
④
<imgwidth="54"height="22"v:shapes="_x0000_i1255"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds04.files/image329.png">
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