(Solved): It is not D. Let \( \mathbf{v}_{1}=\left[\begin{array}{r}0 \\ 0 \\ -4\end{array}\right], \mathbf{v} ...

It is not D.

Let \( \mathbf{v}_{1}=\left[\begin{array}{r}0 \\ 0 \\ -4\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}0 \\ -5 \\ 12\end{array}\right] \), and \( \mathbf{v}_{3}=\left[\begin{array}{r}6 \\ -4 \\ -8\end{array}\right] \). Does \( \left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\} \) span \( \mathbb{R}^{3} \) ? Why or why not? Choose the correct answer below. A. Yes. When the given vectors are written as the columns of a matrix \( \mathrm{A}, \mathrm{A} \) has a pivot position in every row. B. Yes. Any vector in \( \mathbb{R}^{3} \) except the zero vector can be written as a linear combination of these three vectors. C. No. The set of given vectors spans a plane in \( \mathbb{R}^{3} \). Any of the three vectors can be written as a linear combination of the other two. D. No. When the given vectors are written as the columns of a matrix \( \mathrm{A}, \mathrm{A} \) has a pivot position in only two rows.