Exercise 3.5.1

(a) Row and column space dimensions $=5$, nullspace dimension $=4,\dim <!--\; FUNCTION\; APPLICATION\; -->\left(N\left(A^T\right)\right)$ $=2\mathrm{sum}<!--\; FUNCTION\; APPLICATION\; -->5+5+4+2=16=m+n$

(b) Column space is $R^3$; left nullspace contains only $0$.