1. If a, a, a span S and b, b, b span S, find a basis for...

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

$$a₁ = \begin{bmatrix} 1 \\ 3 \\ 2 \\ -1 \end{bmatrix}; a₂ = \begin{bmatrix} 0 \\ -1 \\ 2 \\ 1 \end{bmatrix}; a₃ = \begin{bmatrix} 2 \\ 7 \\ 2 \\ -3 \end{bmatrix};$$

$$b₁ = \begin{bmatrix} 1 \\ 8 \\ 0 \\ -4 \end{bmatrix}; b₂ = \begin{bmatrix} 2 \\ 9 \\ -2 \\ -5 \end{bmatrix}; b₃ = \begin{bmatrix} 1 \\ 0 \\ -1 \\ 3 \end{bmatrix}$$