线性代数极大无关组求解 线性代数极大无关组问题求解？
\u7ebf\u6027\u4ee3\u6570\u6c42\u6781\u5927\u65e0\u5173\u7ec41 2 0 -1 3
1 0 2 1 -1
0 -1 1 1 -2
2 3 1 -2 4
\u7b2c4\u884c, \u51cf\u53bb\u7b2c1\u884c\u00d72
1 2 0 -1 3
1 0 2 1 -1
0 -1 1 1 -2
0 -1 1 0 -2
\u7b2c2\u884c, \u51cf\u53bb\u7b2c1\u884c\u00d71
1 2 0 -1 3
0 -2 2 2 -4
0 -1 1 1 -2
0 -1 1 0 -2
\u7b2c4\u884c, \u51cf\u53bb\u7b2c2\u884c\u00d712
1 2 0 -1 3
0 -2 2 2 -4
0 -1 1 1 -2
0 0 0 -1 0
\u7b2c3\u884c, \u51cf\u53bb\u7b2c2\u884c\u00d712
1 2 0 -1 3
0 -2 2 2 -4
0 0 0 0 0
0 0 0 -1 0
\u7b2c3\u884c\u4ea4\u6362\u7b2c4\u884c
1 2 0 -1 3
0 -2 2 2 -4
0 0 0 -1 0
0 0 0 0 0
\u7b2c3\u884c, \u63d0\u53d6\u516c\u56e0\u5b50-1
1 2 0 -1 3
0 -2 2 2 -4
0 0 0 1 0
0 0 0 0 0
\u7b2c2\u884c, \u63d0\u53d6\u516c\u56e0\u5b50-2
1 2 0 -1 3
0 1 -1 -1 2
0 0 0 1 0
0 0 0 0 0
\u7b2c1\u884c,\u7b2c2\u884c, \u52a0\u4e0a\u7b2c3\u884c\u00d71,1
1 2 0 0 3
0 1 -1 0 2
0 0 0 1 0
0 0 0 0 0
\u7b2c1\u884c, \u52a0\u4e0a\u7b2c2\u884c\u00d7-2
1 0 2 0 -1
0 1 -1 0 2
0 0 0 1 0
0 0 0 0 0
\u5219\u5411\u91cf\u7ec4\u79e9\u4e3a3\uff0c\u5411\u91cf\u7ec4\u7ebf\u6027\u76f8\u5173\uff0c\u4e14\u03b11, \u03b12, \u03b14\u662f\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u662f\u5411\u91cf\u7a7a\u95f4\u7684\u4e00\u7ec4\u57fa\uff0c\u5176\u7ef4\u6570\u662f3\u03b13=2\u03b11-\u03b12\u03b15=-\u03b11+2\u03b12
a3 -a1 -2a2 = 0
a4 -2a1 -a2 = (0,0,-1,0)
a5-2a1 -a2 +a4 -2a1 -a2 =0
\u6240\u4ee5\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u4e3a(a1,a2,a4),
a3 =a1 +2a2
a5 = 4a1 +2a2 -a4
[ 1, 2, 1, 3]
[ -1, 1, -1, 0]
[ 0, 5, -2, 7]
[ 4, 6, 0, k]
化为行最简矩阵：
A =
[ 1, 2, 1, 3]
[ 0, 1, 0, 1]
[ 0, 0, -1, 1]
[ 0, 0, 0, 3*k - 42]
当3*k - 42 = 0时线性相关
即当 k = 14 时，向量组线性相关
当 k = 14 时
A =
1 2 1 3
-1 1 -1 0
0 5 -2 7
4 6 0 14
化为行最简矩阵：
1 0 0 2
0 1 0 1
0 0 1 -1
0 0 0 0
∴极大无关组：a1,a2,a3
a4 = 2a1 + a2 - a3
答题不易，请及时采纳，谢谢！
线性相关则行列式为0或者秩<4
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