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# Help with vector geometry

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Consider the vectors $$\mathbf{v} = \begin{pmatrix} 1\\3 \end{pmatrix}, \mathbf{w} = \begin{pmatrix} 3\\2 \end{pmatrix}$$, and $$\mathbf{x} = \begin{pmatrix}1 \\ 0 \end{pmatrix}.$$ If the vectors $$\mathbf{v}, \mathbf{w} \text{ and }\mathbf{x}$$ are linearly independent, answer with 0. If they aren't, find coefficients a,b, and c, not all 0, such that $$a \begin{pmatrix} 1 \\ 3 \end{pmatrix} + b \begin{pmatrix} 3 \\ 2 \end{pmatrix} + c \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix}0 \\ 0 \end{pmatrix}$$ and answer with $$\dfrac{a+b}{c}$$

Jun 5, 2019