Let U=span{(1,3,−2,2,3),(1,4,−3,4,2),(2,3,−1,−2,9),(2,4,−2,0,8)}U=\operatorname{span}\{(1,3,-2,2,3),(1,4,-3,4,2),(2,3,-1,-2,9),(2,4,-2,0,8)\}U=span{(1,3,−2,2,3),(1,4,−3,4,2),(2,3,−1,−2,9),(2,4,−2,0,8)} and W=span{(1,3,0,2,1),(1,5,−6,6,3),(2,5,3,2,1),(2,7,−3,6,3)}W=\operatorname{span}\{(1,3,0,2,1),(1,5,-6,6,3),(2,5,3,2,1),(2,7,-3,6,3)\}W=span{(1,3,0,2,1),(1,5,−6,6,3),(2,5,3,2,1),(2,7,−3,6,3)} be two subspaces of R5\mathbb{R}^5R5. The dimension of U∩WU \cap WU∩W is
