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Merge pull request #645 from JoinB-AI/patch-2
Update chapter08.md
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docs/linalg/chapter08.md

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讨论$b$满足什么条件才能让方程$Ax=b$有解(solvability condition on b):当且仅当$b$属于$A$的列空间时。另一种描述:如果$A$的各行线性组合得到$0$行,则$b$端分量做同样的线性组合,结果也为$0$时,方程才有解。
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解法:令所有自由变量取$0$,则有$
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\Big\lbrace
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\begin{eqnarray*}
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\begin{cases}
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x_1 & + & 2x_3 & = & 1 \\
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& & 2x_3 & = & 3 \\
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\end{eqnarray*}
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\end{cases}
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$
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,解得
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$
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\Big\lbrace
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\begin{eqnarray*}
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,解得$
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\begin{cases}
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x_1 & = & -2 \\
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x_3 & = & \frac{3}{2} \\
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\end{eqnarray*}
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\end{cases}
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$
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,代入$Ax=b$求得特解
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$
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$。
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令$Ax=b$成立的所有解:
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$$
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\Big\lbrace
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\begin{eqnarray}
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\begin{cases}
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A & x_p & = & b \\
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A & x_n & = & 0 \\
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\end{eqnarray}
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\end{cases}
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\quad
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\underrightarrow{两式相加}
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\quad

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