给定向量组 $\boldsymbol{\alpha}_1=\left(\begin{array}{lll}1 & 1 & 1\end{array}\right), \boldsymbol{\alpha}_2=\left(\begin{array}{lll}a & 0 & b\end{array}\right), \boldsymbol{\alpha}_3=\left(\begin{array}{lll}1 & 3 & 2\end{array}\right)$ ，若 $\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3$ 线性相关，则 $a, b$ 满足关系式