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191问答库 > 四元费其次线性方程组Ax=b的系数矩阵A的秩为2，它的3个解向量为n1=(4,3,2,1)^T,n2=(1,3,5,1)^T,

四元费其次线性方程组Ax=b的系数矩阵A的秩为2，它的3个解向量为n1=(4,3,2,1)^T,n2=(1,3,5,1)^T,

n3=(-2,6,3,2)求该方程组的通解

2025-03-16 10:13:48

推荐回答（1个）

回答1：

四元非齐次线性方程组 Ax=b 的系数矩阵 A 的秩为 2，
则导出组 Ax=0 有 4-2=2 个基础解系，
n1-n3=(6, -3, -1, -1)^T， n2-n3=(3, -3, 2, -1)^T,
满足 Ax=0，且线性无关，故是 Ax=0 的基础解系。
Ax=b 的通解为 x=(4, 3, 2, 1)^T+k1(6, -3, -1, -1)^T+k2(3, -3, 2, -1)^T。
其中 k1，k2 为任意常数。

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