Inside R4\mathbb{R}^4R4, define
U={(x1,x2,x3,x4) : x1+x2+x3+x4=0 and x1−x2+x3−x4=0}U = \{(x_1, x_2, x_3, x_4) \ : \ x_1 + x_2 + x_3 + x_4 = 0 \ \text{ and } \ x_1 - x_2 + x_3 - x_4 = 0\}U={(x1,x2,x3,x4) : x1+x2+x3+x4=0 and x1−x2+x3−x4=0}
W=span{(1, 0, −1, 0), (0, 1, 0, −1), (1, 1, −1, −1)}W = \operatorname{span}\{(1,\,0,\,-1,\,0),\ \ (0,\,1,\,0,\,-1),\ \ (1,\,1,\,-1,\,-1)\}W=span{(1,0,−1,0), (0,1,0,−1), (1,1,−1,−1)}
One subspace is described by equations, the other by generators. What is dim(U∩W)\dim(U \cap W)dim(U∩W)?
Select all that apply.
333
222
111
000