{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-18-06-s2010-exam1-q2",
    "area": "mathematics",
    "topic": "linear-algebra",
    "origin": "external",
    "title": "Nullspace, column space, pivots, and block structure",
    "skills": [
      "matrix-operations",
      "linear-systems",
      "row-reduction",
      "subspaces",
      "rank",
      "rank-nullity"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 14,
    "prerequisites": [
      "linear-systems",
      "reduced-row-echelon-form"
    ],
    "source_id": "mit-18-06-s2010",
    "locator": {
      "document": "Quiz 1 (listed by OCW as Exam 1)",
      "label": "Question 2(a–c)",
      "page": 2,
      "solution_pages": "2–3"
    },
    "links": {
      "problem": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam1_s10/",
      "solution": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam1_s10_sol/"
    },
    "selection_note": "Distinguishes procedural row reduction from geometric understanding of the four fundamental subspaces.",
    "answer_status": "official-solution"
  }
}