Answer: Ax = 0.
- A Ax = x
- B Ax = 0
- C A<sup>T</sup> x = 0
- D Ax = b for some b
Correct answer: B. Ax = 0
Explanation: The null space (kernel) is defined as Ker(A) = {x : Ax = 0}. By rank-nullity theorem, dim(Ker A) = n − rank(A). It is the solution set of the homogeneous system, always containing the zero vector. Answer: Ax = 0.
Element aij of matrix A sits at the intersection of row i and column j.
Concept context
Matrix operations, determinants, inverses, and solving linear systems