# One reduction, four structural conclusions

> ML Prep screening item.

- Stable ID: `math-la-02-system-subspaces`
- Collection: screening
- Area: Mathematics
- Topic: Linear Algebra
- Origin: original
- Difficulty: easy
- Expected time: 5 minutes
- Skills: linear-systems, row-reduction, rank, subspaces, rank-nullity
- Item JSON: https://mlprep.iwase.dev/item/math-la-02-system-subspaces.json

## Problem

For
$$
A=\begin{bmatrix}1&2&3\\2&4&6\end{bmatrix},\qquad b=\begin{bmatrix}1\\2\end{bmatrix},
$$
row-reduce $[A\mid b]$. Give the rank of $A$, a basis for its column space,
a basis for its nullspace, and the full solution of $Ax=b$. Verify rank-nullity.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-la-02-system-subspaces`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.