# Symmetry, orthogonality, and eigenspaces

> ML preparation item.

- Stable ID: `mit-18-06-s2010-exam3-q1`
- Area: Mathematics
- Topic: Linear Algebra
- Origin: external
- Expected time: 16 minutes
- Skills: symmetric-matrices, orthogonal-matrices, eigenvalues, diagonalization, trace
- Item JSON: https://mlprep.iwase.dev/data/items/mit-18-06-s2010-exam3-q1.json

This site does not reproduce the third-party problem.

- Source: MIT 18.06 Linear Algebra
- Document: Quiz 3 (listed by OCW as Exam 3)
- Locator: Question 1(a–d), page 1
- Official answer PDF page(s): 1
- Original problem: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam3_s10/
- Official answer: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam3_s10_soln/
- Answer status: official-solution


## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `mit-18-06-s2010-exam3-q1`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.