I'm watching the video tutorial on spans here: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/linear_combinations/v/linear-combinations-and-span
At 8:13, he says that the vectors a = [1,2] and b = [0,3] span R2. Visually, I can see it. But I tried to work it out, like so:
sp(a, b) = x[1,2] + y[0,3] such that x,y exist in R = [x, 2x] + [0, 3y] st x,y e R = [x, 2x + 3y] st x,y e R
With that said, how do we know that
[x, 2x + 3y]spans R2? I tried picking a random point ([19, 6]) and let x=19 and solved for y (2*19 + 3y = 6) and found that when x=19 and y=-10, then I can get the point [19, 6].
But I'm confused as to how would I be able to find out that
[x, 2x + 3y] can make any and all points in R2? What's my next step in determining if it spans R2?