# Certify a quadratic form

> ML Prep screening item.

- Stable ID: `math-la-07-quadratic-positive`
- Collection: screening
- Area: Mathematics
- Topic: Linear Algebra
- Origin: original
- Difficulty: hard
- Expected time: 5 minutes
- Skills: quadratic-forms, positive-definite-semidefinite
- Item JSON: https://mlprep.iwase.dev/item/math-la-07-quadratic-positive.json

## Problem

Consider $q(x,y)=2x^2-2xy+2y^2$. Write $q=z^{\mathsf T}Hz$, determine whether
$H$ is positive definite, and find the minimum of $q$ over $x^2+y^2=1$.


## 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-07-quadratic-positive`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.