# Nullspace, column space, pivots, and block structure

> ML Prep practice item.

- Stable ID: `mit-18-06-s2010-exam1-q2`
- Collection: practice
- Area: Mathematics
- Topic: Linear Algebra
- Origin: external
- Difficulty: medium
- Expected time: 14 minutes
- Skills: matrix-operations, linear-systems, row-reduction, subspaces, rank, rank-nullity
- Item JSON: https://mlprep.iwase.dev/item/mit-18-06-s2010-exam1-q2.json

- Source: MIT 18.06 Linear Algebra
- Document: Quiz 1 (listed by OCW as Exam 1)
- Locator: Question 2(a–c), page 2
- Official answer PDF page(s): 2–3
- Original problem: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam1_s10/
- Official answer: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/mit18_06s10_exam1_s10_sol/
- 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-exam1-q2`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.