Exercise 3.5.3

Row space basis $=$ first two rows of $U$; column space basis $=$ pivot columns (of $A$ not $U$ ) $=(1,1,0)$ and $(3,4,1)$; nullspace basis $(1,0,0,0,0),(0,2,-1,0,0),(0,2,0,-2,1)$; left nullspace $(1,-1,1)=$ last row of $E^{-1}=L$.