If anyone could explain how the following is done, it would be greatly appreciated!
*Note that (+) denotes the vector addition symbol (which is displayed in textbooks as a circle with a plus sign inside it)
Here is a vector space candidate. We have as our set, R^2, as our vector addition x (+) y = (x1, x2) (+) (y1, y2) = (x1y1, x2y2) and as our scalar multiplication a * x = a * (x1, x2) = (a + x1, a + x2). Verify the following vector space axiom.
a * (x (+) y) = (a * x) (+) (a * y)