Let V subspace of R3 with inner product V={(x,y,z) in R3 : x+z=0, y=2x}

1. how can we find the projection P onto V

2. how can we find the projection matrix P as of the normal basis of R3

3. how can we find a basis of R3 for which the matrix P will be $\displaystyle \left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right)$

Thanks in advance!!