1. ## Finding the projection

Hello,

projw x, where x = (1,2,0,-1) W is the subspace of R^4 spanned by the vectors.

v1 = (1/2,1/2,1/2,1/2)
v2 = (1/2,1/2,-1/2,-1/2)
v3 = (1/2,-1/2,1/2,-1/2)

Thanks!

2. $Project_{~\vec{v}}~\vec{x} = <\vec{x},\vec{v}>\displaystyle\frac{\vec{v}}{\|\ve c{v}\|}$

$\mathfrak{B}_W = span(\vec{v}_1,~\vec{v}_2,~\vec{v}_3)$

$Project_{~W}~\vec{x}=\sum\limits_{i=1}^3 Project_{~\vec{v}_i}~\vec{x}=\displaystyle\frac{1} {2}\left[\begin{array}{c} 3\\ 3\\ -1\\ -1 \end{array}\right]$

3. can you elaborate more on the 3rd line?