Consider the matrix A=[123400120000]A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{bmatrix}A=100200310420
What is rank(A)\text{rank}(A)rank(A) and nullity(A)\text{nullity}(A)nullity(A)?
rank(A)=2,nullity(A)=2\text{rank}(A) = 2, \text{nullity}(A) = 2rank(A)=2,nullity(A)=2
rank(A)=3,nullity(A)=1\text{rank}(A) = 3, \text{nullity}(A) = 1rank(A)=3,nullity(A)=1
rank(A)=2,nullity(A)=1\text{rank}(A) = 2, \text{nullity}(A) = 1rank(A)=2,nullity(A)=1
rank(A)=3,nullity(A)=0\text{rank}(A) = 3, \text{nullity}(A) = 0rank(A)=3,nullity(A)=0