Show that \(w\) is in the subspace of \(\mathbb{R}^4\) spanned by \(v_1\), \(v_2\), and \(v_3\), where these vectors are defined as follows.
\(w = \begin{bmatrix} 21 \\ -18 \\ 6 \\ 46 \end{bmatrix}\), \(v_1 = \begin{bmatrix} 4 \\ -6 \\ -3 \\ 11 \end{bmatrix}\), \(v_2 = \begin{bmatrix} -4 \\ 2 \\ -2 \\ -9 \end{bmatrix}\), \(v_3 = \begin{bmatrix} -9 \\ 8 \\ -5 \\ -17 \end{bmatrix}\)
To show that \(w\) is in the subspace, express \(w\) as a linear combination of \(v_1\), \(v_2\), and \(v_3\)
The vector \(w\) is in the subspace spanned by \(v_1\), \(v_2\), and \(v_3\). It is given by the formula \(w = \boxed{}v_1 + \boxed{}v_2 + \boxed{}v_3\)
(Simplify your answers. Type integers or fractions.)