Let AAA be an m×nm \times nm×n matrix with rank(A)=r\text{rank}(A) = rrank(A)=r. By the Rank-Nullity Theorem, what is nullity(A)\text{nullity}(A)nullity(A)?
nullity(A)=m−r\text{nullity}(A) = m - rnullity(A)=m−r
nullity(A)=n−r\text{nullity}(A) = n - rnullity(A)=n−r
nullity(A)=m+n−r\text{nullity}(A) = m + n - rnullity(A)=m+n−r
nullity(A)=r\text{nullity}(A) = rnullity(A)=r