well, no, but: what can you say if A maps every basis element of a basis for onto the line y = 2x?
conversely, given a point (t,2t) on the line, can you find some element (x,y) with A(x,y) = (t,2t)?
Show that multiplication by
maps every point in the plane onto the line .
I tried to see what happens with the unit square and the points in the unit square is easy to see that they maps onto the line . But does that equals that every point in the plane maps onto the line?
/regards
well, no, but: what can you say if A maps every basis element of a basis for onto the line y = 2x?
conversely, given a point (t,2t) on the line, can you find some element (x,y) with A(x,y) = (t,2t)?