线性方程组 System of linear equations

（重定向自Homogeneous system）

La intersección de dos planos que no son paralelos coincidentes es una recta.

线性方程组是数学方程组的一种，它符合以下的形式：

\begin{cases}a_{1,1}x_{1} + a_{1,2}x_{2} + \cdots + a_{1,n}x_{n}= b_{1} \\ a_{2,1}x_{1} + a_{2,2}x_{2} + \cdots + a_{2,n}x_{n}= b_{2} \\ \vdots \quad \quad \quad \vdots \\ a_{m,1}x_{1} + a_{m,2}x_{2} + \cdots + a_{m,n}x_{n}= b_{m} \end{cases}

其中的 $a_{1,1}, \, a_{1,2}$ 以及 $b_{1}, \, b_{2}$ 等等是已知的常数，而 $x_{1}, \, x_{2}$ 等等则是要求的未知数。

如果用线性代数中的概念来表达，则线性方程组可以写成：

\mathbf{A} \mathbf{x} = \mathbf{b}

这里的A是m×n 矩阵，x是含有n个元素列矢量，b是含有m 个元素列矢量。

A= \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix},\quad \bold{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \bold{b}= \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}

这是线性方程组的另一种记录方法。在已知矩阵 $A$ 和矢量 $\mathbf{b}$ 的情况求得未知矢量 $\mathbf{x}$ 是线性代数的基本问题之一。

单词	Homogeneous system
释义	Homogeneous system 中文百科线性方程组 System of linear equations （重定向自Homogeneous system）线性方程组是数学方程组的一种，它符合以下的形式： $\begin{cases}a_{1,1}x_{1} + a_{1,2}x_{2} + \cdots + a_{1,n}x_{n}= b_{1} \\ a_{2,1}x_{1} + a_{2,2}x_{2} + \cdots + a_{2,n}x_{n}= b_{2} \\ \vdots \quad \quad \quad \vdots \\ a_{m,1}x_{1} + a_{m,2}x_{2} + \cdots + a_{m,n}x_{n}= b_{m} \end{cases}$ 其中的 $a_{1,1}, \, a_{1,2}$ 以及 $b_{1}, \, b_{2}$ 等等是已知的常数，而 $x_{1}, \, x_{2}$ 等等则是要求的未知数。如果用线性代数中的概念来表达，则线性方程组可以写成： $\mathbf{A} \mathbf{x} = \mathbf{b}$ 这里的A是m×n 矩阵，x是含有n个元素列矢量，b是含有m 个元素列矢量。 $A= \begin{bmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{bmatrix},\quad \bold{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \bold{b}= \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}$ 这是线性方程组的另一种记录方法。在已知矩阵 $A$ 和矢量 $\mathbf{b}$ 的情况求得未知矢量 $\mathbf{x}$ 是线性代数的基本问题之一。英语百科 System of linear equations 线性方程组（重定向自Homogeneous system） In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. For example, is a system of three equations in the three variables $x, y, z$ . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by
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Homogeneous system

线性方程组 System of linear equations

System of linear equations 线性方程组