The Given Set Is a Basis for a Subspace W

question 19

Multiple Choice

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W.
-Let $\mathrm { x } _ { 1 } = \left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \mathrm { x } _ { 2 } = \left[ \begin{array} { r } 1 \\ 1 \\ - 1 \\ - 1 \end{array} \right] , \mathrm { x } _ { 3 } = \left[ \begin{array} { l } 1 \\ 0 \\ 1 \\ 1 \end{array} \right]$

• A) \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ 4 \\ - 4 \\ - 2 \end{array} \right] , \left[ \begin{array} { r } 18 \\ 4 \\ 19 \\ 13 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 0 \\ 0 \\ - 2 \end{array} \right] , \left[ \begin{array} { l } 6 \\ 0 \\ 1 \\ 3 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 1 \\ - 1 \\ - 1 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 0 \\ 1 \\ 1 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r } 0 \\ 1 \\ - 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ 2 \\ - 2 \\ - 4 \end{array} \right] , \left[ \begin{array} { r } 14 \\ 2 \\ 9 \\ 7 \end{array} \right]\)

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