求极大无关组，并将其余向量由该极大无关组线性表出 求向量组的秩，并确定一个极大无关组，将其余向量用该极大无关组...
\u6c42\u5411\u91cf\u7ec4\u7684\u79e9\u548c\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c\u5e76\u5c06\u5176\u4f59\u5411\u91cf\u7528\u8be5\u6781\u5927\u65e0\u5173\u7ec4\u7ebf\u6027\u8868\u51fa\uff0c\uff083\uff09\uff084\uff09\u4e24\u5c0f\u9898\u8981\u5177\u4f53\u8fc7\u7a0b\u8c22\u8c221 2 3 -1 2
0 4 -4 -2 10
1 0 -3 2 -1
2 3 5 -1 0
r3-r1,r4-2r1
1 2 3 -1 2
0 4 -4 -2 10
0 -2 -6 3 -3
0 -1 -1 1 -4
r1+2r4,r2+4r4,r3-2r4,r4*(-1)
1 0 1 1 -6
0 0 -8 2 -6
0 0 -4 1 5
0 1 1 -1 4
r1-r3,r2-2r3,r4+r2
1 0 5 0 -11
0 0 0 0 -16
0 0 -4 1 5
0 1 -3 0 9
r2*(-1/16),r1+11r2,r3-5r2,r4-9r2
1 0 5 0 0
0 0 0 0 1
0 0 -4 1 0
0 1 -3 0 0
\u5411\u91cf\u7ec4\u7684\u79e9\u4e3a4, a1,a2,a4,a5 \u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4
\u4e14 a3 = 5a1-3a2-4a4
\u79e9\u4e3a2 A1 A2\u65e0\u5173 A3=1.5A1+0.5A2 A4=2A1+A2
1 2 3 0-1 -2 0 3
2 4 6 0
1 2 -1 -4
r2+r1,r3-2r1,r4-r1
1 2 3 0
0 0 3 3
0 0 0 0
0 0 -4 -4
r1-r2,r2*(1/3),r4+4r2
1 2 0 -3
0 0 1 1
0 0 0 0
0 0 0 0
所以α1,α3是一个极大无关组, 且
α2 = 2α1, α4 = -3α1+α3.
你给的矩阵是否是由向量组作为列向量构成的矩阵?
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0 2 -7 4 0 0 0 0 0 0 0 0 1 0 3/2 1 0 1 -7/2 2 0 0 0 0 0 0 0 0 {a,b} 鏋佸ぇ绾挎鏃犲叧缁 c=3/2a-7/2b d=a+2b
绛旓細1 1 -2 3 3 -1 8 1 1 3 -9 7 r2-r1,r3-3r1,r4-r1 1 -1 5 -1 0 2 -7 4 0 2 -7 4 0 4 -14 8 r3-r2,r4-2r2, r2*(1/2),r2+r1 1 0 3/2 1 0 1 -7/2 2 0 0 0 0 0 0 0 0 伪1,伪2 鏄竴涓鏋佸ぇ鏃犲叧缁 ...
绛旓細鎴戜滑鍙互浣跨敤楂樻柉娑堝厓娉曟潵姹備竴涓悜閲忕粍鐨勪竴涓鏈澶ф棤鍏崇粍锛屽苟寰楀埌鍏朵綑鍚戦噺鐨勭嚎鎬ц〃绀恒傚凡鐭ュ悜閲忕粍涓猴細147258369 灏嗗悜閲忕粍涓殑姣忎釜鍚戦噺浣滀负鐭╅樀鐨勪竴鍒楋紝褰㈡垚涓涓煩闃礎銆傚A杩涜楂樻柉娑堝厓锛屽嵆瀵笰杩涜鍒濈瓑琛屽彉鎹紝灏嗗叾鍖栦负琛岄樁姊舰寮忋傛牴鎹闃舵褰㈠紡锛屽彲浠ョ‘瀹氭瘡涓湭鐭ユ暟鐨勭郴鏁般傚皢寰楀埌鐨勭郴鏁颁唬鍏ュ搴旂殑绛夊紡...
绛旓細鐢盿1,a2,a3浣滀负鍒鍚戦噺鏋勯犵煩闃 1 -2 5 3 2 -1 3 10 -17 鐢ㄥ垵绛夎鍙樻崲鍖栨垚 1 0 1 0 1 -2 0 0 0 鏋佸ぇ鏃犲叧缁涓篴1,a2, 涓 a3 = a1-2a2 婊℃剰璇烽噰绾砠_^
绛旓細銆愮瓟妗堛戯細鏋佸ぇ鏃犲叧缁涓猴細伪1锛屛2锛屛4锛屼笖伪3=3伪1+伪2锛屛5=-伪1-伪2+伪4$伪2锛屛3锛屛4涓烘瀬澶ф棤鍏崇粍伪1=伪2+伪3+伪4
绛旓細r3-r4 0 2 1 0 0 0 0 -2 0 2 1 -2 1 -1 1 1 r3-r1-r2, r4-r1 0 2 1 0 0 0 0 -2 0 0 0 0 1 -3 0 1 浜ゆ崲琛 1 -3 0 1 0 2 1 0 0 0 0 -2 0 0 0 0 a1,a3,a4 鏄鏋佸ぇ鏃犲叧缁 a2 = -3a1+2a3+0a4....
绛旓細0 5 0 -11 0 0 0 0 -16 0 0 -4 1 5 0 1 -3 0 9 r2*(-1/16),r1+11r2,r3-5r2,r4-9r2 1 0 5 0 0 0 0 0 0 1 0 0 -4 1 0 0 1 -3 0 0 鍚戦噺缁鐨勭З涓4, a1,a2,a4,a5 鏄竴涓鏋佸ぇ鏃犲叧缁 涓 a3 = 5a1-3a2-4a4 ...
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_^ ...
