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📐 Mathematics  ·  Matrices  ·  JEE

The null space (kernel) of matrix A consists of all vectors x such that:

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.

Matrix A (3 rows x 3 columns)a11a12a13a21a22a23a31a32a33column 1column 2column 3row 1row 2row 3

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

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