$$ \left\{
\begin{aligned}
{\beta _1} &= {\alpha _1}\\
{\beta _2} &= {\alpha _2} - \frac{{\left( {{\alpha _2},{\beta _1}} \right)}}{{\left( {{\beta _1},{\beta _1}} \right)}}{\beta _1}\\
&\cdots \cdots \\
{\beta _n} &= {\alpha _n} - \frac{{\left( {{\alpha _n},{\beta _1}} \right)}}{{\left( {{\beta _1},{\beta _1}} \right)}}{\beta _1} - \frac{{\left( {{\alpha _n},{\beta _2}} \right)}}{{\left( {{\beta _2},{\beta _2}} \right)}}{\beta _2} - \cdots - \frac{{\left( {{\alpha _n},{\beta _{n - 1}}} \right)}}{{\left( {{\beta _{n - 1}},{\beta _{n - 1}}} \right)}}{\beta _{n - 1}}
\end{aligned}
\right.
$$

方程组左对齐