第1个回答 2023-06-24
线性方程组的解集合的极大线性无关组就是这个方程组的基础解系。先求解方程组解出所有解向量,然后求出其极大线性无关组就好。一般求基础解系先把系数矩阵进行初等变换成下三角矩阵,然后得出秩,确定自由变量,得到基础解系,基础解系是相对于齐次(等号右边为0)的.例如:x1+x2+x3+7x4=2,x1+2x2+x3+2x4=3,5x1+8x2+5x3+20x4=13,2x1+5x2+2x3-x4=7,其增广矩阵为11172121235852013252-17通过初等变换为:11172010-510000000000秩为2,未知数个数为4,自由变量个数为4-2=2设自由变量为x3、x4,取(x3,x4)=(1,0)和(0,1)代入方程组(取最终变换得到的比较简单)可得:(x1,x2)=(-1,0)和(-12,5)于是基础解系的基:(-1,0,1,0)T和(-12,5,0,1)T.扩展资料线性代数通解和基[tele.yrui88.com.cn/article/760829.html]
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