Exercise 3.5.17

Row space $=\mathit{yz}$ plane; column space $=\mathit{xy}$ plane; nullspace $=x$ axis; left nullspace $=z$ axis. For $I+A$ : Row space $=$ column space $=R^3$, both nullspaces contain only the zero vector. 18 Row $3-2$ row $2+$ row $1=$ zero row so the vectors $c(1,-2,1)$ are in the left nullspace. The same vectors happen to be in the nullspace (an accident for this matrix).