{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-18-06-s2010-exam3-q3c",
    "area": "mathematics",
    "topic": "linear-algebra",
    "origin": "external",
    "title": "Singular value decomposition from the Gram matrix",
    "skills": [
      "svd",
      "orthogonality"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 10,
    "prerequisites": [
      "eigenvalues",
      "orthogonality"
    ],
    "source_id": "mit-18-06-s2010",
    "locator": {
      "document": "Quiz 3 (listed by OCW as Exam 3)",
      "label": "Question 3(c)",
      "page": 3,
      "solution_pages": "3"
    },
    "links": {
      "problem": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam3_s10/",
      "solution": "https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam3_s10_soln/"
    },
    "selection_note": "A compact check that the learner can construct an SVD from the eigendecomposition of a Gram matrix.",
    "source_caveat": "The official solution's explanatory sentence reverses conventional left/right singular-vector labels, although its displayed factor matrices are consistent with the standard SVD.",
    "answer_status": "official-solution"
  }
}