Let $\mathbf{v}$ and $\mathbf{w}$ be vectors such that
\[\operatorname{proj}_{\mathbf{w}} \mathbf{v} = \begin{pmatrix} 1 \\ 0 \\ -3 \end{pmatrix}.\]Compute $\operatorname{proj}_{\mathbf{w}} (-2 \mathbf{v}).$
Question:
Let $\mathbf{v}$ and $\mathbf{w}$ be vectors such that
\[\operatorname{proj}_{\mathbf{w}} \mathbf{v} = \begin{pmatrix} 1 \\ 0 \\ -3 \end{pmatrix}.\]Compute $\operatorname{proj}_{\mathbf{w}} (-2 \mathbf{v}).$
Answer:
Let's think step by step.

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\begin{pmatrix} -2 \\ 0 \\ 6 \end{pmatrix}
Let $\mathbf{v}$ and $\mathbf{w}$ be vectors such that
\[\operatorname{proj}_{\mathbf{w}} \mathbf{v} = \begin{pmatrix} 1 \\ 0 \\ -3 \end{pmatrix}.\]Compute $\operatorname{proj}_{\mathbf{w}} (-2 \mathbf{v}).$
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