Let $\displaystyle \phi: R^3 \rightarrow R^3$ be the projection of the three-dimensional space onto the plane $\displaystyle x + y + z = 0$. Find the matrix of this linear transformation in the standard basisi,j,k.

[Hint: Find the coordinates of the normal vectorNto the plane. Then use the fact that the projection of a basis vectorm(m=i,j, ork) onto the plane ism - awhereais the projection ofmonto the direction ofN.]