(Solved): Algebra Let \( \mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3} \in \mathbb{R}^{3} \) be distinct an ...

Algebra Let \( \mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3} \in \mathbb{R}^{3} \) be distinct and non-zero. Let \( U=\operatorname{span}\left\{\mathbf{v}_{1}, \mathbf{v}_{\mathbf{2}}\right\} \) and let \( V=\operatorname{span}\left\{\mathbf{v}_{2}, \mathbf{v}_{3}\right\} \). Out of \( 0,1,2,3 \), which are the possible values of the dimension of the subspace \( U \cap V \) ? You must give reasons to support your claims, for values which are possible you need just give specific values for the vectors and give a basis for \( U \cap V \), for values which are not possible you must explain why.