QuestionLet $u, w, v_{1}, v_{2}$, and $v_{3}$ be the vectors in $\mathbb{R}^{4}$ defined by $$u=\left[\begin{array}{l} 17 \\ 12 \\ 16 \\ 10 \end{array}\right] \quad w=\left[\begin{array}{c} 29 \\ 12 \\ -29 \\ 14 \end{array}\right] \quad v_{1}=\left[\begin{array}{c} 7 \\ -2 \\ 6 \\ -19 \end{array}\right] \quad v_{2}=\left[\begin{array}{c} -2 \\ -19 \\ 1 \\ -18 \end{array}\right] \quad v_{3}=\left[\begin{array}{c} 6 \\ -8 \\ -11 \\ -1 \end{array}\right]$$ (a) Is $u \in \operatorname{span}\left\{v_{1}, v_{2}, v_{3}\right\}$ ? Write all zeros if it is not in the span or write zero as a non-trivial (not all zero coefficients) linear combination of $u_{1}, v_{1}, v_{2}$, and $v_{3}$ if $u$ is in the span. $$0=\square u+\square v_{1}+\square v_{2}+\square v_{3}$$ (b) Is $w \in \operatorname{span}\left\{v_{1}, v_{2}, v_{3}\right\}$ ? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of $w$, $v_{1}, v_{2}$, and $v_{3}$ if $w$ is in the span. $$0=\square w+\square v_{1}+\square v_{2}+\square v_{3}$$ (c) Type the dimension of $\operatorname{span}\left\{v_{1}, v_{2}, v_{3}, u\right\}$ : $\square$