[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"$fcMvB--wQ07oWjplbwSHWVu5U-fMMFI52J56yWSykvEg":3},{"answer":4,"createTime":5,"id":6,"options":7,"origin":12,"question":19,"related":20,"source":24,"type":25},[],"2023-06-18 00:00:25",68683765,[8,9,10,11],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F275a207fb4538c43036333e99313f9e7.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd1459ff36e6a037b02c3d9dae4cd6e1c.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F0561c2500e536c0f6634ef4e304ff951.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ff5f489d2264239d589532034811a9973.png\">",{"count":13,"courseId":14,"courseImg":15,"courseName":16,"workId":17,"workName":18},83,"1018d23ffa818f474966003a64cbf236","https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F77805ba0eda3de29c4fcaa5d951e158b.jpg","高等代数","work_28200233","第七章 线性变换(选择题)(25题)","数域P上全体n阶方阵组成的线性空间V上的两个线性变换\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd3ded8acfa9994a8519ad3b2c005bb95.png\">、\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F3856c537885c466f12bf6680f4b4e1e8.png\">定义为:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1bd966a7532f3143f358cd1d39d260dc.png\">,\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1a5c59e37365e44643568927cadad3e0.png\">,\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F97c0822987140e31a93e7bd2e89bb362.png\">,则\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F635a644b8f07bbe53131121e12665414.png\">为",[21,26,35,44,53,62,71,80,89,98],{"answer":22,"createTime":5,"id":6,"options":23,"question":19,"source":24,"type":25},[],[8,9,10,11],"v1",0,{"answer":27,"createTime":5,"id":28,"options":29,"question":34,"source":24,"type":25},[],68683766,[30,31,32,33],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F763cd66dd27668376d39809ea99e5c0d.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F193d74dc20847ef7e660cedbdeb1116c.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F69c32054d2bbcbc2c28427d458913bcf.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F210637a22672754e705404ea3be3d969.png\">","下列各变换\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F6ecde00f734004019f53ccac72669b86.webp\">上的线性变换的是",{"answer":36,"createTime":5,"id":37,"options":38,"question":43,"source":24,"type":25},[],68683767,[39,40,41,42],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc38b898e2be2df64fc893d131ffa6b3f.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F322b5636a4a70ceda11e1a01dcde9f22.png\">的特征根","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fcc4c69030ae7a42a43ded04361a6e0ba.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F322b5636a4a70ceda11e1a01dcde9f22.png\">的特征向量","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F33a0088c8252985f9bec3c7894a924f7.png\">与\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1a62b9f8c0c3320901d70a17acee7bed.png\">线性无关","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F33a0088c8252985f9bec3c7894a924f7.png\">与\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1a62b9f8c0c3320901d70a17acee7bed.png\">线性相关","设\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F322b5636a4a70ceda11e1a01dcde9f22.png\">是线性空间V上的一个线性变换,\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F749c8b45470df36bb50f86259f654cbc.png\">、\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fbc413a7e7df4e2a18ec520baa0569123.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd3ded8acfa9994a8519ad3b2c005bb95.png\">的两个不同特征根,\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F33a0088c8252985f9bec3c7894a924f7.png\">、\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1a62b9f8c0c3320901d70a17acee7bed.png\">分别为\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd3ded8acfa9994a8519ad3b2c005bb95.png\">的属于\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F749c8b45470df36bb50f86259f654cbc.png\">、\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fbc413a7e7df4e2a18ec520baa0569123.png\">的特征向量,则",{"answer":45,"createTime":5,"id":46,"options":47,"question":52,"source":24,"type":25},[],68683768,[48,49,50,51],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1985eaeb8087824b39eb9af95ceb88c1.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F969ccf3b9e8784ca389a6f514e60d21a.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F53728ce2aa2dc2065d5d97d3260fdf2f.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc5b1d50f24f2a5ca751c5e6d0bfb3d9d.webp\">","设可逆矩阵A一个特征值为2,则\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F59cbb632f5fa28ffe0c1539404a7dbc9.webp\">有一个特征值为",{"answer":54,"createTime":5,"id":55,"options":56,"question":61,"source":24,"type":25},[],68683769,[57,58,59,60],"A有n个线性无关的特征向量","A可逆","A的n个特征值互不相同","A无零特征值","n阶矩阵A与对角矩阵相似的充要条件是",{"answer":63,"createTime":5,"id":64,"options":65,"question":70,"source":24,"type":25},[],68683770,[66,67,68,69],"若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa57605141c2ccbef0a47678e1435c41e.png\">是可逆变换,则它在任何一组基下的矩阵都是可逆矩阵","若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fb30f0e20c5dc0d3a84f2c372a2431c7a.png\">线性无关,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc793f152d14e1c04d949f9dbdfa2af10.png\">也线性无关","若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F14d672af777be80510d59769e2939f1e.png\">在某组基下的矩阵是对角矩阵,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F88bbd8e4291ffe260fd1ec5a3decb3f4.png\">有n个互不相同的特征值","必定存在一组基,使得 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F14d672af777be80510d59769e2939f1e.png\">在这组基下的矩阵是对角矩阵","设 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\"> 是数域P上n维线性空间\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F43cba1a756cf73262150be4dcc55b5d7.png\">上的线性变换,则",{"answer":72,"createTime":5,"id":73,"options":74,"question":79,"source":24,"type":25},[],68683771,[75,76,77,78],"设σ在某组基下的矩阵是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F152b35092201fc3a9190bff9ff1f9819.png\">,且\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Faf3c58ee737e716089cbfc1fa238f031.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\">的特征值,则线性方程组\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F8ddea108ed9d58326365bdda0d2ca3f0.png\">的解空间就是不变子空间\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ffe240e9efdda30f3f855162ee7e1c45d.png\">","在σ在某组基下的矩阵是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F152b35092201fc3a9190bff9ff1f9819.png\">,若线性方程组\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F7d2d2780e141e897f6b37313a7cc60bc.png\">有非零解,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F7f22ee000dbad73ab3d437c1fedc36ca.png\">是σ的特征值","若\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fbb1e7a5215cec84730236e22267d34b8.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\">的特征值,则特征子空间\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ffe240e9efdda30f3f855162ee7e1c45d.png\">必定不是零空间","若V的所有特征子空间的和等于V,则必定存在V的一组基使得 σ 在这组基下的矩阵是对角矩阵","设 σ 是数域P上n维线性空间V上的线性变换,下列说法错误的是",{"answer":81,"createTime":5,"id":82,"options":83,"question":88,"source":24,"type":25},[],68683772,[84,85,86,87],"若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F6e619f0c9e9337326f65d41175611753.png\">和 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F186c79272a5ebcf9a767f3a88aa8c747.png\">线性相关,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61987e2f03f12f0463ecbbf404ec8df1.png\">","若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fb2fa6015685f554ff06e2e500d8ab9ea.png\">,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa469291f406a0af57d746c09342aea6c.png\">和 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F186c79272a5ebcf9a767f3a88aa8c747.png\">线性相关","若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa469291f406a0af57d746c09342aea6c.png\">和 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F186c79272a5ebcf9a767f3a88aa8c747.png\">线性无关,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61987e2f03f12f0463ecbbf404ec8df1.png\">","若 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61987e2f03f12f0463ecbbf404ec8df1.png\">,则 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa469291f406a0af57d746c09342aea6c.png\">和 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F186c79272a5ebcf9a767f3a88aa8c747.png\">线性无关","设\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc776dcf3d08e7d1a9b8f5afb0581ff18.png\">是数域P上线性空间V的线性变换,\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa469291f406a0af57d746c09342aea6c.png\">和\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F186c79272a5ebcf9a767f3a88aa8c747.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F7036e5d34b6d61f2389d765d50152ecd.png\">的分别属于特征值\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fbf39ff2aeb947424e458ca9119a62c33.png\">的特征向量,那么­",{"answer":90,"createTime":5,"id":91,"options":92,"question":97,"source":24,"type":25},[],68683773,[93,94,95,96],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F81a5d2200c6a23fedab7676810a20be0.png\">","(\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1a93822960da871be69faadfa7c654dc.png\">)","(\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F2b0bd1a580bf7402bd21d2097cbd8e49.png\">)","(\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F8a0eee8e63d70ca87e14f04cc86f310d.png\">)","线性变换\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F70fb25c01ef05b0676fceabc95a9e12e.png\">: \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F17332c3297fcd694e1c9391174eca741.png\">下的矩阵是",{"answer":99,"createTime":5,"id":100,"options":101,"question":106,"source":24,"type":25},[],68683774,[102,103,104,105],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F39d1ffa1b5ab40ea56c1bc71e10d8f38.png\">线性无关","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ff316a07fb470530a31cb2d10f24ccb34.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa30e9e43661f8bc140c53aa049c066dc.png\">是 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fb8de5dc0971b506ab85e4f7c84d9bd8d.png\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F7e2fa24a0525b5e6bc2a7884d67dc2b6.png\">是 \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\">的特征向量","设\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc871d84fb6ab25f5619e1bf7350e96be.png\">是分别属于\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F61f515f42030a60730d09ca23ab00c03.png\">的两两不同的特征根\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F67a5bb0cec48b1388f37214b2697e93a.png\">的特征向量.其中\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F5b1d066a441a241b5b8aa137b467d181.png\">V是向量空间,则下列结论正确的是"]