求极大无关组并把其余向量表示出来。a1=1 -2 5. a2=3 2 -1. a3=3 10 -17.手机党...
\u8bbe\u5411\u91cf\u7ec4a1,a2,a3,\u7ebf\u6027\u65e0\u5173\u3002\u8bc1\u660e\uff1a\u5411\u91cf\u7ec4a1+a2+a3,a2+a3,a3\u4e5f\u7ebf\u6027\u65e0\u5173\u5047\u8bbea1+a2+a3,a2+a3,a3\u7ebf\u6027\u76f8\u5173\uff0c
\u5219k1\uff08a1+a2+a3\uff09+k2\uff08a2+a3\uff09+k3a3=0\u5176\u4e2dk1\u3001k2\u3001k3\u4e0d\u5168\u4e3a0.
\u5316\u7b80\u6210k1a1+\uff08k1+k2\uff09a2+\uff08k1+k2+k3\uff09a3=0
\u7531\u4e8e\u5411\u91cf\u7ec4a1,a2,a3,\u7ebf\u6027\u65e0\u5173\u3002
\u6240\u4ee5k1=0\u3001k1+k2=0\u3001k1+k2+k3=0
\u5219k1=0\u3001k2=0\u3001k3=0
\u4e0e\u4e0a\u8ff0k1\u3001k2\u3001k3\u4e0d\u5168\u4e3a0\u77db\u76fe\u3002
\u6240\u4ee5\u5411\u91cf\u7ec4a1+a2+a3,a2+a3,a3\u4e5f\u7ebf\u6027\u65e0\u5173
\u8bc1\u660e: \u8bbe k1(a1+a3)+k2(a2+a3)+k3a3=0
\u5f97: k1a1+k2a2+(k1+k2+k3)a3=0
\u7531 a1,a2,a3\u7ebf\u6027\u65e0\u5173
\u5f97 k1=0,k2=0, k1+k2+k3=0
\u6240\u4ee5\u6709 k1=k2=k3=0
\u6240\u4ee5 a1+a3,a2+a3,a3 \u7ebf\u6027\u65e0\u5173
1 -2 5
3 2 -1
3 10 -17
用初等行变换化成
1 0 1
0 1 -2
0 0 0
极大无关组为a1,a2, 且 a3 = a1-2a2
满意请采纳^_^
列个矩阵，【a1 a2 a3】，然后进行初等行变换，变换成阶梯型矩阵（就是求秩），不同阶梯上的向量就是线性无关的。 呃！就是一楼那样的！话说，a1和a3也是极大无关组。最好两组都写上，作为两种情况！嘎嘎，有趣。
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绛旓細0 -2 4 2 1 1 -1 0 r2*(1/5),r1-3r2,r3-4r2,r4+r2 0 2 0 2 0 0 1 1 0 -2 0 -2 1 1 0 1 r3+r1,r1*(1/2),r4-r1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 鎵浠 a1,a2,a3 鏄竴涓鏋佸ぇ鏃犲叧缁 涓 a4 = a2+a3.
绛旓細鍐欏嚭鍚戦噺缁涓 2 -1 3 8 1 1 1 5 1 7 -1 9 1 10 -2 11 r1-2r2,r3-r2,r4-r2 锝0 -3 1 -2 1 1 1 5 0 6 -2 4 0 9 -3 6 r3+2r1,r4+3r1,r2-r1,浜ゆ崲r1r2 ~1 4 0 7 0 -3 1 -2 0 0 0 0 0 0 0 0 浜庢槸寰楀埌鏋佸ぇ鏃犲叧缁涓篴1,a3锛岃宎2=4a1 -3a3锛宎4=...
绛旓細1 0 0 2 0 1 0 -1 1 0 1 3 1 -1 -3 0 r3-r1,r4-r1 1 0 0 2 0 1 0 -1 0 0 1 1 0 -1 -3 -2 r3+r2+3r3 1 0 0 2 0 1 0 -1 0 0 1 1 0 0 0 0 鎵浠ノ1,伪2,伪3鏄竴涓鏋佸ぇ鏃犲叧缁, 伪4=2伪1-伪2+伪3...
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 ...
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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 鏄竴涓鏋佸ぇ鏃犲叧缁 a2 = ...
绛旓細姹俛1,a2,a3,a4鐨勭浉鍏虫,骞舵眰鍏舵瀬澶ф棤鍏崇粍,骞跺皢鍏朵綑鍚戦噺鐢鏋佸ぇ鏃犲叧缁勮〃绀灏嗙煩闃靛啓涓(a1,a2,a3,a4)鐨勫舰寮:1 3 2 2 2 2 3 2 3 1 1 2-1 -1 1 -1灏嗙涓琛屽垎鍒箻浠-2,-3,1鍐嶅姞鍒扮浜,涓,鍥涜涓1 3 2 2 0 -4 -1 -2 0 -8 -5 -40 2 3 1缁х画杩涜琛屽彉鎹,灏嗙浜岃涔樹互-2,1/...
绛旓細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 鍚戦噺缁鐨勭З: 3 (闈為浂琛屾暟)鏈澶ф棤鍏崇粍: a1,a2,a4 (闈為浂琛岄闈為浂鍏冩墍鍦ㄥ垪)鍏朵綑琛ㄧず: a3 = a1 - a2 + 0a3.婊℃剰璇烽噰绾砠_^ ...
