求向量组的一个极大无关组，并将其余向量用此极大无关组线性表示 求下列向量组的一个极大无关组，并将其余向量用此极大无关组线性...
\u6c42\u4e00\u4e2a\u5411\u91cf\u7ec4\u7684\u6781\u5927\u65e0\u5173\u7ec4\u8981\u600e\u4e48\u6c42\uff1f\u5e76\u628a\u5176\u4f59\u5411\u91cf\u7528\u6b64\u7ebf\u6027\u65e0\u5173\u7ec4\u8868\u793a\u89e3\uff1a\uff08a1\uff3eT\uff0ca2\uff3eT\uff0ca3\uff3eT\uff0ca4\uff3eT\uff09\uff1d
1111
1102
100\uff0d3
r1\uff0dr2\uff0cr2\uff0dr3
001\uff0d1
0105
100\uff0d3
r1r3
100\uff0d3
0105
001\uff0d1
\u6240\u4ee5a1\uff0ca2\uff0ca3\u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c\u4e14a4\uff1d\uff0d3a1\uff0b5a2\uff0da3\uff0e
\uff08a1\uff3eT\uff0ca2\uff3eT\uff0ca3\uff3eT\uff0ca4\uff3eT\uff09\uff1d
1111
1102
100\uff0d3
r1\uff0dr2\uff0cr2\uff0dr3
001\uff0d1
0105
100\uff0d3
r1r3
100\uff0d3
0105
001\uff0d1
\u6240\u4ee5a1\uff0ca2\uff0ca3\u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c\u4e14a4\uff1d\uff0d3a1\uff0b5a2\uff0da3\uff0e
\u6700\u7b80\u5355\u7684\u5c31\u662f\u628a\u7ebf\u5f62\u65e0\u5173\u7684\u51e0\u4e2a\u5316\u6210\u5bf9\u89d2\u5168\u90e8\u4e3a1\u5176\u4ed6\u4e3a0\uff0c\u8fd9\u662f\u57fa\u4e8e\u5355\u4f4d\u77e9\u9635\u7684\u6240\u6709\u5411\u91cf\u53ef\u4ee5\u8868\u793a\u4efb\u610f\u5411\u91cf\uff0c\u4e00\u4e0b\u5c31\u51fa\u6765\u4e86\uff0c\u8fd9\u4e2a\u5fc5\u987b\u77e5\u9053\uff0c\u4ee5\u540e\u57fa\u7840\u89e3\u6790\u90e8\u5206\u66f4\u8981\u77e5\u9053\u3002
\u6269\u5c55\u8d44\u6599
\u89e3\u9898\u6b65\u9aa4\uff1a
\u7b2c\u4e00\u6b65\uff1a\u5c31\u662f\u5316\u884c\u9636\u68af\u5f62\u77e9\u9635\uff0c\u76f4\u5230\u5316\u6210\u5404\u9636\u7b2c\u4e00\u4e2a\u4e0d\u4e3a0\u7684\u6570\u6240\u5728\u7684\u5217\u5176\u4f59\u5404\u503c\u5747\u4e3a0\u7684\u5f62\u5f0f\u3002
\u7b2c\u4e8c\u90e8\uff1a\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u5404\u4e2a\u5355\u4f4d\u5217\uff08\u6bcf\u5217\u4e2d\u53ea\u6709\u4e00\u4e2a1\uff09\u770b\u505a\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u8fd9\u4e9b\u5217\u4e13\u4e1a\u672f\u8bed\u53eb\u505a\u6807\u51c6\u5217\u3002
\u7b2c\u4e09\u6b65\uff1a\u4e5f\u5c31\u662f\u7528\u6807\u51c6\u5217\u6765\u8868\u793a\u5176\u4f59\u5404\u5217\uff0c\u76f8\u5f53\u4e8e\u975e\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u57fa\u7840\u89e3\u7cfb\u3002\u6709\u4e00\u4e2a\u5f88\u7b80\u5355\u7684\u65b9\u6cd5\u5c31\u662f\u6298\u73b0\u6cd5\uff0c\u4e0d\u77e5\u9053LZ\u662f\u5426\u77e5\u9053\u3002\u4f46\u662f\u6700\u6700\u666e\u901a\u7684\u65b9\u6cd5\u4e5f\u53ef\u4ee5\u7b97\u51fa\u6765\u3002
\u5411\u91cf\u7ec4\u7684\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4
\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\uff08maximal linearly independent system\uff09\u662f\u5728\u7ebf\u6027\u7a7a\u95f4\u4e2d\u62e5\u6709\u5411\u91cf\u4e2a\u6570\u6700\u591a\u7684\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u7ec4\u3002
\u4e00\u4e2a\u5411\u91cf\u7ec4\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u662f\u5176\u6700\u672c\u8d28\u7684\u90e8\u5206, \u5bf9\u8bb8\u591a\u95ee\u9898\u7684\u7814\u7a76\u8d77\u7740\u975e\u5e38\u91cd\u8981\u7684\u4f5c\u7528\u3002\u5982\u786e\u5b9a\u77e9\u9635\u7684\u79e9, \u8ba8\u8bba\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u57fa\u7840\u89e3\u7cfb\u7b49\u3002
\u57fa\u672c\u6027\u8d28
\uff081\uff09\u53ea\u542b\u96f6\u5411\u91cf\u7684\u5411\u91cf\u7ec4\u6ca1\u6709\u6781\u5927\u65e0\u5173\u7ec4\u3002
\uff082\uff09\u4e00\u4e2a\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u7ec4\u7684\u6781\u5927\u65e0\u5173\u7ec4\u5c31\u662f\u5176\u672c\u8eab\u3002
\uff083\uff09\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u5bf9\u4e8e\u6bcf\u4e2a\u5411\u91cf\u7ec4\u6765\u8bf4\u5e76\u4e0d\u552f\u4e00\uff0c\u4f46\u662f\u6bcf\u4e2a\u5411\u91cf\u7ec4\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u90fd\u542b\u6709\u76f8\u540c\u4e2a\u6570\u7684\u5411\u91cf\u3002
\uff084\uff09\u9f50\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3\u5411\u91cf\u7684\u6781\u5927\u65e0\u5173\u7ec4\u4e3a\u57fa\u7840\u89e3\u7cfb\u3002
\uff085\uff09\u4efb\u610f\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u90fd\u4e0e\u5411\u91cf\u7ec4\u672c\u8eab\u7b49\u4ef7\u3002
5 4 1 3
2 1 1 4
-3 -2 -1 -1
1 3 -2 2
目标:用行变换化最简形 (过程省了 有问题消息我)
1 0 1 0
0 1 -1 0
0 0 0 1
0 0 0 0
向量组的秩: 3 (非零行数)
最大无关组: a1,a2,a4 (非零行首非零元所在列)
其余表示: a3 = a1 - a2 + 0a3.
满意请采纳^_^
绛旓細2 -1 3 8 1 1 1 5 1 7 -1 9 1 10 -2 11 r1-2r2,r3-r2,r4-r2 0 -3 1 -2 1 1 1 5 0 6 -2 4 0 9 -3 6 r3+2r1,r4+3r1,r2-r1 0 -3 1 -2 1 4 0 7 0 0 0 0 0 0 0 0 鎵浠 a1,a3 鏄涓涓瀬澶ф棤鍏崇粍 a2 = ...
绛旓細0 -1 1 -3 -7 0 -2 2 -6 -10 r1+r3,r2-2r3,r4-2r3 1 0 2 1 -6 0 0 0 0 12 0 -1 1 -3 -7 0 0 0 0 4 --> 1 0 2 1 0 0 1 -1 3 0 0 0 0 0 1 0 0 0 0 0 a1,a2,a5 鏄鏋佸ぇ鏃犲叧缁 a3=2a1-a2 a4=a1...
绛旓細~0 3 -3 6 0 -1 1 -2 0 2 2 2 1 0 2 -1 r1+3r2,r3/2,r2+r3 ~0 0 0 0 0 0 2 -1 0 1 1 1 1 0 2 -1 r4-r2,r2/2,r3-r2锛屼氦鎹㈣娆″簭 ~1 0 0 0 0 1 0 3/2 0 0 1 -1/2 0 0 0 0 鎵浠鏋佸ぇ鏃犲叧缁涓篴1,a2,a3锛岀З=3 ...
绛旓細5 4 1 3 2 1 1 4 -3 -2 -1 -1 1 3 -2 2 鐩爣:鐢ㄨ鍙樻崲鍖栨渶绠褰 (杩囩▼鐪佷簡 鏈夐棶棰樻秷鎭垜)1 0 1 0 0 1 -1 0 0 0 0 1 0 0 0 0 鍚戦噺缁勭殑绉: 3 (闈為浂琛屾暟)鏈澶鏃犲叧缁: a1,a2,a4 (闈為浂琛岄闈為浂鍏冩墍鍦ㄥ垪)鍏朵綑...
绛旓細姹備笅鍒鍚戦噺缁勭殑涓涓鏈澶鏃犲叧缁a1=(1,2,3,-4),a2=(2,3,-4,1)a3=(2,-5,8,-3)a4=(5,26.-9,-12)a5=(3,-4,1,2)... 姹備笅鍒楀悜閲忕粍鐨勪竴涓渶澶ф棤鍏崇粍a1=(1,2,3,-4),a2=(2,3,-4,1)a3=(2,-5,8,-3)a4=(5,26.-9,-12)a5=(3,-4,1,2) 灞曞紑 鎴戞潵绛 1...
绛旓細鍒濈瓑琛屽彉鎹负 [1 0 0 -3][0 1 1 4][0 0 -1 1]鍒濈瓑琛屽彉鎹负 [1 0 0 -3][0 1 0 5][0 0 1 -1]a1,a2,a3 涓涓涓瀬澶绾挎鏃犲叧缁銆俛4 = -3a1+5a2-a3
绛旓細鈹 -1 1 -3 -3鈹 鈹0 2 -2 0鈹 鈹0 0 2 2鈹 鈹0 0 1 1鈹 鈹 2 0 6 8鈹 鈹0 0 0 0鈹 鈹0 0 0 0鈹 鈹0 0 0 0鈹 鈶-鈶,鈶-2[鈶+鈶 鈶+2鈶★紝鈶+鈶 R(A)=3,鈭磋鍚戦噺缁勭殑涓涓瀬澶绾挎鏃犲叧缁鐢变笁涓悜閲忕粍鎴愶紝...
绛旓細,r2+3r3,r4+2r3 1 4 -1 2 0 0 2 -3 0 3 1 0 0 0 -2 3 r4+r3 1 4 -1 2 0 0 2 -3 0 3 1 0 0 0 0 0 浜ゆ崲琛 1 4 -1 2 0 3 1 0 0 0 2 -3 0 0 0 0 鍚戦噺缁勭殑绉╀负3, a1,a2,a3 鏄涓涓瀬澶ф棤鍏崇粍.
绛旓細1 0 2 3 0 1 -1 0 0 0 0 0 0 0 7 7 r3*(1/7)1 0 2 3 0 1 -1 0 0 0 0 0 0 0 1 1 r1-2r4, r2+r4 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 a1,a2,a3 鏄涓涓瀬澶绾挎鏃犲叧缁 a4 = a1+a2+a3 ...
绛旓細AX0锛孉涓轰簲涓鍚戦噺鐨鍒楁帓鍒椼傛眰x鍗冲彲銆
