【单选题】【消耗次数：1】
对于齐次线性方程组以下说法正确的是（）
①
若<imgwidth="54"height="20"v:shapes="_x0000_i1352"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">有解，则必有<imgwidth="54"height="22"v:shapes="_x0000_i1353"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image439.png">
②
若<imgwidth="54"height="20"v:shapes="_x0000_i1354"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">无解，则必有<imgwidth="54"height="22"v:shapes="_x0000_i1355"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image441.png">
③
若<imgwidth="54"height="20"v:shapes="_x0000_i1356"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">有非零解，则必有<imgwidth="54"height="22"v:shapes="_x0000_i1357"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image439.png">
④
<imgwidth="54"height="20"v:shapes="_x0000_i1358"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">总有解
参考答案：
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相关题目
【单选题】
若<imgwidth="18"height="18"v:shapes="_x0000_i1305"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image110.png">是<imgwidth="34"height="18"v:shapes="_x0000_i1306"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image380.png">矩阵，<imgwidth="54"height="20"v:shapes="_x0000_i1307"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">是<imgwidth="54"height="20"v:shapes="_x0000_i1308"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image331.png">的导出组，则（）
①
若<imgwidth="54"height="20"v:shapes="_x0000_i1309"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image331.png">有无穷多个解，则<imgwidth="54"height="20"v:shapes="_x0000_i1310"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">仅有零解
②
<imgwidth="54"height="20"v:shapes="_x0000_i1311"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">仅有零解，则<imgwidth="54"height="20"v:shapes="_x0000_i1312"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image331.png">有唯一解
③
若<imgwidth="54"height="20"v:shapes="_x0000_i1313"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image331.png">有无穷多个解，则<imgwidth="54"height="20"v:shapes="_x0000_i1314"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">有非零解
④
<imgwidth="54"height="20"v:shapes="_x0000_i1315"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">有非零解，则<imgwidth="54"height="20"v:shapes="_x0000_i1316"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image331.png">有无穷多个解
【单选题】
设有<imgwidth="22"height="22"v:shapes="_x0000_i1198"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image242.png">中两组基<imgwidth="70"height="26"v:shapes="_x0000_i1199"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image226.png">和<imgwidth="70"height="26"v:shapes="_x0000_i1200"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image244.png">，已知<imgwidth="206"height="28"v:shapes="_x0000_i1201"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image246.png"><imgwidth="70"height="28"v:shapes="_x0000_i1202"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image248.png">；<imgwidth="270"height="28"v:shapes="_x0000_i1203"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image250.png">，则从基<imgwidth="70"height="26"v:shapes="_x0000_i1204"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image226.png">到基<imgwidth="70"height="26"v:shapes="_x0000_i1205"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image244.png">的过渡矩阵为（）
①
<imgwidth="102"height="84"v:shapes="_x0000_i1206"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image252.png">
②
<imgwidth="102"height="84"v:shapes="_x0000_i1207"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image254.png">
③
<imgwidth="112"height="84"v:shapes="_x0000_i1208"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image256.png">
④
<imgwidth="110"height="84"v:shapes="_x0000_i1209"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image258.png">
【单选题】
已知向量<imgwidth="288"height="114"v:shapes="_x0000_i1294"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image366.png">，若<imgwidth="18"height="22"v:shapes="_x0000_i1295"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image368.png">可由<imgwidth="70"height="26"v:shapes="_x0000_i1296"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image279.png">线性表出那么（）
①
<imgwidth="45"height="22"v:shapes="_x0000_i1297"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image371.png">，<imgwidth="49"height="22"v:shapes="_x0000_i1298"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image373.png">
②
<imgwidth="45"height="22"v:shapes="_x0000_i1299"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image371.png">，<imgwidth="49"height="22"v:shapes="_x0000_i1300"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image373.png">
③
<imgwidth="45"height="22"v:shapes="_x0000_i1301"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image375.png">，<imgwidth="49"height="22"v:shapes="_x0000_i1302"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image373.png">
④
<imgwidth="45"height="22"v:shapes="_x0000_i1303"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image371.png">，<imgwidth="49"height="22"v:shapes="_x0000_i1304"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image377.png">
【单选题】
已知<imgwidth="66"height="84"v:shapes="_x0000_i1256"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image318.png">和<imgwidth="80"height="84"v:shapes="_x0000_i1257"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image320.png">是线性方程组<imgwidth="54"height="20"v:shapes="_x0000_i1258"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">的两个解，则系数矩阵<imgwidth="18"height="18"v:shapes="_x0000_i1259"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image260.png">是（）
①
<imgwidth="102"height="84"v:shapes="_x0000_i1260"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image323.png">
②
<imgwidth="96"height="58"v:shapes="_x0000_i1261"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image325.png">
③
<imgwidth="96"height="58"v:shapes="_x0000_i1262"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image327.png">
④
<imgwidth="106"height="84"v:shapes="_x0000_i1263"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image329.png">
【单选题】
已知<imgwidth="18"height="18"v:shapes="_x0000_i1285"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image110.png">是<imgwidth="14"height="16"v:shapes="_x0000_i1286"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image264.png">阶方阵，且<imgwidth="70"height="28"v:shapes="_x0000_i1287"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image305.png">，则<imgwidth="18"height="18"v:shapes="_x0000_i1288"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image110.png">的<imgwidth="14"height="16"v:shapes="_x0000_i1289"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image264.png">个行向量中（）
①
任意<imgwidth="14"height="14"v:shapes="_x0000_i1290"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image362.png">个行向量线性无关
②
必有<imgwidth="14"height="14"v:shapes="_x0000_i1291"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image362.png">个行向量线性无关
③
任一行向量都可由其余<imgwidth="36"height="18"v:shapes="_x0000_i1292"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image364.png">个行向量线性表出
④
任意<imgwidth="14"height="14"v:shapes="_x0000_i1293"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image362.png">个行向量都为极大无关组
【单选题】
已知<imgwidth="138"height="26"v:shapes="_x0000_i1327"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image398.png">，则<imgwidth="70"height="24"v:shapes="_x0000_i1328"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image400.png">为（）
①
<imgwidth="96"height="26"v:shapes="_x0000_i1329"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image402.png">
②
<imgwidth="98"height="26"v:shapes="_x0000_i1330"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image404.png">
③
<imgwidth="126"height="26"v:shapes="_x0000_i1331"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image406.png">
④
<imgwidth="166"height="28"v:shapes="_x0000_i1332"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image408.png">
【单选题】
已知<imgwidth="202"height="24"v:shapes="_x0000_i1076"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image084.png">,且有<imgwidth="134"height="24"v:shapes="_x0000_i1077"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image086.png">,则（）
①
<imgwidth="138"height="46"v:shapes="_x0000_i1078"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image088.png">
②
<imgwidth="128"height="46"v:shapes="_x0000_i1079"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image090.png">
③
<imgwidth="128"height="46"v:shapes="_x0000_i1080"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image092.png">
④
<imgwidth="150"height="46"v:shapes="_x0000_i1081"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image094.png">
【单选题】
设<imgwidth="18"height="18"v:shapes="_x0000_i1106"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image130.png">是<imgwidth="44"height="16"v:shapes="_x0000_i1107"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image132.png">矩阵，则齐次线性方程<imgwidth="54"height="20"v:shapes="_x0000_i1108"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image134.png">仅有零解的充分必要条件是（）
①
<imgwidth="18"height="18"v:shapes="_x0000_i1109"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image130.png">的行向量组线性无关
②
<imgwidth="18"height="18"v:shapes="_x0000_i1110"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image130.png">的行向量组线性相关
③
<imgwidth="18"height="18"v:shapes="_x0000_i1111"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image130.png">的列向量组线性无关
④
<imgwidth="18"height="18"v:shapes="_x0000_i1112"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image130.png">的列向量组线性相关
【单选题】
设4个3维列向量<imgwidth="94"height="26"v:shapes="_x0000_i1127"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image146.png">组成的矩阵经初等行变换后变为<imgwidth="266"height="84"v:shapes="_x0000_i1128"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image148.png">，则<imgwidth="22"height="26"v:shapes="_x0000_i1129"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image150.png">可表示为<imgwidth="38"height="26"v:shapes="_x0000_i1130"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image152.png">（）
①
<imgwidth="92"height="26"v:shapes="_x0000_i1131"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image154.png">
②
<imgwidth="120"height="26"v:shapes="_x0000_i1132"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image156.png">
③
<imgwidth="110"height="26"v:shapes="_x0000_i1133"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image158.png">
④
<imgwidth="56"height="26"v:shapes="_x0000_i1134"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image160.png">
【单选题】
若<imgwidth="70"height="26"v:shapes="_x0000_i1276"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image279.png">为齐次线性方程组且<imgwidth="54"height="20"v:shapes="_x0000_i1277"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">的一个基础解系则（）
①
<imgwidth="174"height="26"v:shapes="_x0000_i1278"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image349.png">也是它的一个基础解系
②
基础解系具有唯一性
③
<imgwidth="174"height="26"v:shapes="_x0000_i1279"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image349.png">不一定是<imgwidth="54"height="20"v:shapes="_x0000_i1280"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image297.png">的基础解系
④
以上答案都不对
【单选题】
设<imgwidth="226"height="84"v:shapes="_x0000_i1188"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image228.png">，则线三条直线<imgwidth="142"height="84"v:shapes="_x0000_i1189"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image230.png"><imgwidth="28"height="26"v:shapes="_x0000_i1190"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image232.png"><imgwidth="184"height="30"v:shapes="_x0000_i1191"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image234.png">交于一点的充要条件是（）
①
<imgwidth="70"height="26"v:shapes="_x0000_i1192"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image226.png">线性相关
②
<imgwidth="70"height="26"v:shapes="_x0000_i1193"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image226.png">线性无关
③
秩<imgwidth="98"height="28"v:shapes="_x0000_i1194"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image236.png">秩<imgwidth="62"height="28"v:shapes="_x0000_i1195"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image238.png">
④
<imgwidth="70"height="26"v:shapes="_x0000_i1196"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image226.png">线性相关，<imgwidth="46"height="26"v:shapes="_x0000_i1197"src="http://wljy.whut.edu.cn/uploadfiles/word/xxds03.files/image240.png">线性无关
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