1. If a, a, a span S and b, b, b span S, find a basis for S S. $$a_1 = begin{bmatrix}1 3

1. If a₁, a₂, a₃ span S₁ and b₁, b₂, b₃ span S₂, find a basis for S₁ ∩ S₂.

$$a_1 = \begin{bmatrix}1 \\ 3 \\ -1 \\ 2\end{bmatrix}; a_2 = \begin{bmatrix}0 \\ -1 \\ 2 \\ 1 \end{bmatrix}; a_3 = \begin{bmatrix}2 \\ 7 \\ 2 \\ -3 \end{bmatrix};$$

$$b_1 = \begin{bmatrix}1 \\ 8 \\ 0 \\ -4 \end{bmatrix}; b_2 = \begin{bmatrix}2 \\ 9 \\ -2 \\ -5 \end{bmatrix}; b_3 = \begin{bmatrix}1 \\ 0 \\ -1 \\ 3 \end{bmatrix}.$$