Given that $\displaystyle{ \mathbf{v} = {\left[\begin{array}{c}-6\\2\\-7\\6\\10\\\end{array}\right]}}$, find the coordinates of the orthogonal projection $\displaystyle{ \text{proj}_W(\mathbf{v}) }$ of $\mathbf v$ into the subspace $W$ spanned by $\displaystyle{ \mathbf{u_1}={\left[\begin{array}{c}0\\2\\1\\-1\\1\\\end{array}\right]} }$, $\displaystyle{ \mathbf{u_2}={\left[\begin{array}{c}-7\\3\\5\\16\\5\\\end{array}\right]} }$, $\displaystyle{ \mathbf{u_3}={\left[\begin{array}{c}0\\0\\-1\\0\\1\\\end{array}\right]} }$, $\displaystyle{ \mathbf{u_4}={\left[\begin{array}{c}-4\\-2\\1\\-2\\1\\\end{array}\right]} }$. Note that $\mathbf{u_1}, \mathbf{u_2}, \mathbf{u_3}, \mathbf{u_4}$ are othogonal. $\text{proj}_W(\mathbf{v}) =$$\mathbf{u_1}+$ $\mathbf{u_2}+$ $\mathbf{u_3}+$ $\mathbf{u_4}$ .