If A is a 6 times 8 matrix what is the smallest possible val

If A is a 6 times 8 matrix, what is the smallest possible value for the nullity of A?

Solution

A = 6x8 matrix

lets say 6x8 has 4 pivot columns

so dim null A = 4

so therank of the matrix is 4

and domain space is 8

since the rank and nullity must add to get domain space

so , nullity should be 4