It is said that one-dimensional subspaces of R^2 are just lines through origin.
i) For every such line L, determine the matrix P in standard basis for orthogonal projection onto L. Answer must depend on slope of L.
ii) Now let basis {v1,v2} where v1 is unit vector on line L and v2 is unit vector on line perpendicular to L. Determine matrix of orthogonal projection onto L in basis {v1,v2}.
iii) Now select the favorite line Lthrough origin that is niether vertical, horizontal, nor y=x. In standard basis, determine matrix of one NON-orthogonal projection onto L.