00:01
So we want to prove that the map f of x, y equals x plus y, x is a linear map.
00:09
So let's do the first step, which is to show that f of x1, y1 plus x1, x2, y2, the image of the sum is the sum of the images, x2, y2 is the first step.
00:27
So let's write it down, so the left hand side is f of x1 plus x2, y1 plus y2.
00:37
So by definition this will be sum the first coordinate with the second coordinate, so you get x1 plus x2 plus y1 plus y2, and the second coordinate is just x, so x1 plus x2.
00:57
And now let's just make a simplification, right? so we want to split in x1, y1, so what we want is really x1 plus y1 plus x2 plus y2, and here we already have x1 plus x2...