Let H Be the Hyperplane Through the Points A) $f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=5 x_{1}+6 x_{2}+2 x_{3}+5 x_{4}, d=10$

question 30

Multiple Choice

Let H be the hyperplane through the points. Find a linear functional f and a real number d such that H = [f : d].
- $\left[\begin{array}{l}1 \\ 0 \\ 0 \\ 1\end{array}\right],\left[\begin{array}{l}2 \\ 3 \\ 1 \\ 2\end{array}\right],\left[\begin{array}{r}-1 \\ 1 \\ 2 \\ 1\end{array}\right],\left[\begin{array}{r}3 \\ 2 \\ -1 \\ 1\end{array}\right]$

• A) \( f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=5 x_{1}+6 x_{2}+2 x_{3}+5 x_{4}, d=10 \)
• B) \( f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=x_{1}-2 x_{2}-6 x_{3}+13 x_{4}, d=12 \)
• C) \( f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=2 x_{2}-x_{3}+5 x_{4}, d=5 \)
• D) \( f\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=-5 x_{1}+2 x_{2}-6 x_{3}+5 x_{4}, d=0 \)

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