Let W = S p a n { [ 1 1 1 ] , [ 1 1 − 2 ] } . {\displaystyle W={\rm {Span}}\left\{{\begin{bmatrix}1\\1\\1\end{bmatrix}},\;{\begin{bmatrix}1\\1\\-2\end{bmatrix}}\right\}.}
The following has been calculated already:
p r o j W [ 1 0 0 ] = [ 1 / 2 1 / 2 0 ] . {\displaystyle {\rm {proj}}_{W}{\begin{bmatrix}1\\0\\0\end{bmatrix}}={\begin{bmatrix}1/2\\1/2\\0\end{bmatrix}}.}
Calculate p r o j W [ 0 1 0 ] {\displaystyle {\rm {proj}}_{W}{\begin{bmatrix}0\\1\\0\end{bmatrix}}} and p r o j W [ 0 0 1 ] . {\displaystyle {\rm {proj}}_{W}{\begin{bmatrix}0\\0\\1\end{bmatrix}}.}
and 
