How do the dimensions of the null space and column space of a matrix relate to the number of lead and free variables in the reduced row echelon form of the matrix? ex plain. 3. let a e r6x4 with rk(a) = 4, (a) what is the dimension of null(a)? (b) what is the dimension of col(a)? (c) if be col(a), how many solutions will the linear system ax- b have? 4.