The GATE Grind

GATE Linear Algebra: Vector spaces, linear independence, rank and nullity – Previous Year Questions

4 GATE previous year questions on Vector spaces, linear independence, rank and nullity (Linear Algebra, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

  1. GATE 2024 DA Q47 (2 marks, Multiple select) – Select all choices that are subspaces of R3. Note: R denotes the set of real numbers.
  2. GATE 2025 DA Q25 (1 mark, Multiple select) – Which of the following statements is/are correct?
  3. GATE 2025 DA Q37 (2 marks, Multiple choice) – Let A Rn n be such that A3 = A. Which one of the following statements is ALWAYS correct?
  4. GATE 2026 DA Q22 (1 mark, Multiple choice) – Consider a set S 1 = \x = (x 1, x 2, x 3)T R3 xTx 16\. Let S 2 be another set which is a subspace of R3 with dimension two. Which of the following…