A 4×54 \times 54×5 matrix AAA has 3 pivot columns. Which statements about AAA are true?
rank(A)=3\text{rank}(A) = 3rank(A)=3 and nullity(A)=2\text{nullity}(A) = 2nullity(A)=2
Ax=bA\mathbf{x} = \mathbf{b}Ax=b has a unique solution for all b\mathbf{b}b
Ax=0A\mathbf{x} = \mathbf{0}Ax=0 has only the trivial solution x=0\mathbf{x} = \mathbf{0}x=0
rank(A)=3\text{rank}(A) = 3rank(A)=3 and there are 2 non-pivot columns