求向量组的秩和一个极大无关组，并将其余向量用该极大无关组线性表出，（3）（4）两小题要具体过程谢谢 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...
\u7b2c\uff084\uff09\u9898 \u6c42\u5411\u91cf\u7ec4\u7684\u79e9\u548c\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c\u5e76\u628a\u5176\u4f59\u5411\u91cf\u901a\u8fc7\u6781\u5927\u65e0\u5173\u7ec4\u7ebf\u6027\u8868\u51fa\u3002\u8c22\u8c22\u5927\u5bb6ԅ4. A = (a1, a2, a3, a4) =
[ 0 1 3 -2]
[-1 4 1 2]
[ 2 0 4 -2]
[ 3 -1 2 0]
\u521d\u7b49\u884c\u53d8\u6362\u4e3a
[1 -4 -1 -2]
[0 1 3 -2]
[0 8 6 2]
[0 11 5 6]
\u521d\u7b49\u884c\u53d8\u6362\u4e3a
[1 0 11 -10]
[0 1 3 -2]
[0 0 -18 18]
[0 0 -28 28]
\u521d\u7b49\u884c\u53d8\u6362\u4e3a
[1 0 0 1]
[0 1 0 1]
[0 0 1 -1]
[0 0 0 0]
r(a1, a2, a3, a4) = 3,
a1, a2, a3 \u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c
a4 = a1 + a2 - a3
\u79e9\u4e3a2 A1 A2\u65e0\u5173 A3=1.5A1+0.5A2 A4=2A1+A2
1 2 3 -1 20 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
向量组的秩为4, a1,a2,a4,a5 是一个极大无关组
且 a3 = 5a1-3a2-4a4
绛旓細r2*(1/4), r1-4r2,r3-(t+5)r2 0 2 -2 0 0 0 0 1 0 t 3 0 1 0 2 -1 r1*(1/2),r3-tr1 0 1 -1 0 0 0 0 1 0 0 3+t 0 1 0 2 -1 鎵浠 t=-3鏃, 鍚戦噺缁勭殑绉涓3, a1,a2,a4 鏄涓涓瀬澶ф棤鍏崇粍 t鈮-3鏃, 鍚戦噺缁勭殑绉╀负4, ...
绛旓細1 r3*(1/2),r1-r2 0 0 0 0 0 1 -2 -1 1 0 3/2 1/2 r1<->r3 1 0 3/2 1/2 0 1 -2 -1 0 0 0 0 鎵浠鍚戦噺缁鐨勭З涓2;a1,a2 鏄竴涓瀬澶ф棤鍏崇粍.a3 = (3/2)a1 - 2a2 a4 = (1/2)a1 - a2 婊℃剰璇烽噰绾砠_^ ...
绛旓細鎵浠ョЗ涓 3 銆傜敱浜 a4=a2-a1-a3 锛屾墍浠鏋佸ぇ鏃犲叧缁鍙彇 a1銆乤2銆乤3 銆
绛旓細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 鍚戦噺缁鐨勭З涓3, a1,a2,a3 鏄竴涓瀬澶ф棤鍏崇粍.
绛旓細銆愮瓟妗堛戯細绉╀负3锛浳1锛屛2锛屛3涓涓涓瀬澶ф棤鍏崇粍$绉╀负4锛浳1锛屛2锛屛3锛屛4涓轰竴涓瀬澶ф棤鍏崇粍$绉╀负4锛浳1锛屛2锛屛3锛屛5涓轰竴涓瀬澶ф棤鍏崇粍
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
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