So, given that $$W = \{[x, y] \mid y = |x| \} \in R_2$$ which one is correct, given that vector $v = [x_1,y_1]$ and $u = [x_2,y_2]$ are in $W$? $$ 1.\ v+u = [x_1+x_2, \lVert x_1+x_2 \lVert\ ] $$ $$ 2.\ v+u = [x_1 , \lVert x_1 \lVert\ ] + [x_2 , \lVert x_2 \lVert\ ] = [x_1+x_2, \lVert x_1\lVert + \lVert x_2 \lVert\ ] $$ I don't think they are equal, given that if $x_1 = -1$ and $x_2 = 1$, equation $1$ would give $[0, 0]$ while equation $2$ would give $[0, 2]$.
edit: $$W = \{[x, y] \mid y = |x| \} \in R_2$$