{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-18-06-s2010-exam2-q1",
    "area": "mathematics",
    "topic": "linear-algebra",
    "origin": "external",
    "title": "Projection matrix as geometry and spectrum",
    "skills": [
      "projection",
      "eigenvalues"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 15,
    "prerequisites": [
      "orthogonality",
      "outer-products"
    ],
    "source_id": "mit-18-06-s2010",
    "locator": {
      "document": "Quiz 2 (listed by OCW as Exam 2)",
      "label": "Question 1(a–c)",
      "page": 1,
      "solution_pages": "1–3"
    },
    "links": {
      "problem": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam2_s10/",
      "solution": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam2_s10_soln/"
    },
    "selection_note": "Connects a projection formula to its subspaces and eigenstructure, a high-value ML pattern.",
    "answer_status": "official-solution"
  }
}