设有 $n$ 今未知数 $m$ 今方程的线性方程组
$$ \left{\begin{array}{l} a_{11} x_1+a_{12} x_2+\cdots+a_{1 n} x_n=b_1 \ a_{21} x_1+a_{22} x_2+\cdots+a_{2 n} x_n=b_2 \ \cdots \cdots \cdots \cdots \ a_{m 1} x_1+a_{m 2} x_2+\cdots+a_ x_n=b_m \end{array}\right. $$
其中 $a_$ 是第 $i$ 今方程的第 $j$ 今未知数的系数, $b_i$ 是第 $i$ 今方程的常数项, $i=1,2, \cdots, m$; $j=1,2, \cdots n$, 当常数项 $b_1, b_2, \cdots, b_m$ 不全为零时, 线性方程组 (1) 叫做 $n$ 元非齐次线性方程组, 当 $b_1, b_2, \cdots, b_m$ 全为零时,(1)式成为
$$ \left{\begin{array}{l} a_{11} x_1+a_{12} x_2+\cdots+a_{1 n} x_n=0 \ a_{21} x_1+a_{22} x_2+\cdots+a_{2 n} x_n=0 \ \cdots \cdots \cdots \ a_{m 1} x_1+a_{m 2} x_2+\cdots+a_ x_n=0 \end{array}\right. $$
叫做 $n$ 元齐次线性方程组。将一非齐次线性方程组的常数项改为零所得到的齐次线性方程组称为原方程组的导出组。
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
秩相等,拼接矩阵的秩也相等。
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
定理1 若向量组中含零向量, 则向量组线性相关
定理2 $n$ 个 $n$ 维向量
Initializing MathJax...
Initializing MathJax...
定理3 $n+1$ 个 $n$ 维向量一定线性相关
定理4 向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
定理5 若向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
推论1 若向量组中两个向量对应元素成比例, 则向量组线性相关。
定理6 若向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
定理7 设向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
定理8 若向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
推论2 若向量组
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
线性方程组解的结构
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...
Initializing MathJax...