Show that multiplication by A maps every point in the plane onto the line.

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

Re: Show that multiplication by A maps every point in the plane onto the line.

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)?