How to construct a matrixto project 4-dimensional space to a 2-dimensional plane?

Question

How to Construct a matrix to project vectors in 4-dimensional space to a 2-dimensional plane that lies in the space and passes through the origin and the points (1 ,-1, -1, 1) and (1, -1, 1, 1).

Answer 1

This is matrix [1,1,0,0], becau(1 ,-1, -1, 1) se equation [1,1,0,0] · [x,y,z,t]^T = [0] give us plane x + y = 0 in R² and points (1 ,-1, -1, 1) and (1, -1, 1, 1) inthis plane, because x + y =x + y + 0·z+0·t = 0