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📐 Mathematics  ·  Matrices  ·  JEE

If A is a 3x3 matrix with rank 2, the null space of A has dimension:

Answer: 1.

  • A 3
  • B 2
  • C 0
  • D 1

Correct answer: D. 1

Explanation: Rank-nullity theorem: rank(A) + nullity(A) = number of columns n. Here 2 + nullity = 3, so nullity = 1. The null space is a 1-dimensional subspace (a line through the origin). Answer: 1.

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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