Math Solutions

[Solution] Let S be the orthogonal set S=vecv_1, \vecv_2, \vecv_3. Determine whether \vecp_1 is in Span S, aff S, or conv S. Show all work.

Question: Let \(S\) be the orthogonal set \(S=\left\{\vec{v}_{1}, \vec{v}_{2}, \vec{v}_{3}\right\}\). Determine whether \(\vec{p}_{1}\) is in Span \(S\), aff \(S\), or conv \(S\). Show all work.

\[\vec{v}_{1}=\left[\begin{array}{c} 2 \\ 0 \\ -1 \\ 2 \end{array}\right], \vec{v}_{2}=\left[\begin{array}{c} 0 \\ -2 \\ 2 \\ 1 \end{array}\right], \vec{v}_{3}=\left[\begin{array}{c} -2 \\ 1 \\ 0 \\ 2 \end{array}\right], \vec{p}_{1}=\left[\begin{array}{c} 6 \\ -4 \\ 1 \\ -1 \end{array}\right]\]

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