题目查询

已知向量 $\alpha_1 = \begin{pmatrix}1 \\ 0 \\ 1 \\ 1\end{pmatrix}$, $\alpha_2 = \begin{pmatrix}-1 \\ -1 \\ 0 \\ 1\end{pmatrix}$, $\alpha_3 = \begin{pmatrix}0 \\ 1 \\ -1 \\ 1\end{pmatrix}$, $\beta = \begin{pmatrix}1 \\ 1 \\ 1 \\ -1\end{pmatrix}$, $\gamma = k_1\alpha_1 + k_2\alpha_2 + k_3\alpha_3$。若 $\gamma^T\alpha_i = \beta^T\alpha_i(i=1,2,3)$，则 $k_1^2 + k_2^2 + k_3^2 = \underline{\qquad}$。