Kuest AI

Study anything, free

Start free

Study linear algebra 10x faster with AI

Row reduction, matrices, vector spaces and eigenvalues, taught step by step with pictures of what each matrix actually does to space.

Start freeSee how it teaches

4.87en iOS13,917,000+estudiantes ya estudian con Kuest

topics
10
Course
Intro Linear Algebra
Typical level
College, first or second year
Leads to
Differential equations, machine learning

See how Kuest teaches it

It asks before it tells, so you do the thinking and it sticks.

You: Is v = (1, 1) an eigenvector of A = [[2, 1], [1, 2]]?
Kuest: An eigenvector is a vector that A stretches or shrinks without knocking it off its line. What do you get when you multiply A by v?
You: Av = (2 + 1, 1 + 2) = (3, 3). That isn't (1, 1), so v isn't an eigenvector.
Kuest: Your product is right. Now compare (3, 3) with (1, 1). Do they point in different directions?
You: No, (3, 3) is just 3 times (1, 1). So Av = 3v, which means v is an eigenvector with eigenvalue 3.
Kuest: Exactly. Av only has to land on the same line as v, and the scale factor is the eigenvalue λ.

v is an eigenvector when Av = λv: A scales v without changing its line, and λ is the scale factor.

Students who lock in with Kuest

students
13,917,000+
App Store rating
4.87
countries
100+

  • From a C to an A in chem

    “I stopped copying answers and started actually getting it. My chem grade went from a C to an A in one semester.”

    Junior, Texas

  • 3 hours → 40 minutes

    “My notes turn into a quiz in seconds. What used to take me all night now takes one episode of a show.”

    Sophomore, California

  • Finally ready for the SAT

    “The plan told me exactly what to do each day. I walked in calm for the first time ever.”

    Senior, New York

  • It never lets me skip a step

    “Annoying at first, lifesaver on test day. I could do every problem without it.”

    Freshman, Ohio

  • Better than my tutor

    “It's there at midnight, it's patient, and it costs less than one session with my old tutor.”

    College freshman, Florida

  • My streak is at 94 days

    “The quests are ten minutes. I do them on the bus. Somehow I'm now the one explaining bio to my friends.”

    Junior, Illinois

  • Spanish finally clicked

    “Talking out loud with the tutor fixed my pronunciation faster than a whole year of class.”

    Sophomore, Arizona

  • Found my gaps in one night

    “The gap check showed me I'd never understood moles. Fixed it in 15 minutes.”

    Junior, Georgia

  • Parent here: no more 9pm meltdowns

    “My son gets real help without me pretending I remember calculus, and I can see his progress every week.”

    Parent, Washington

The method

How to study Linear algebra with Kuest

Linear algebra mixes computation with ideas that get abstract fast, so practice both: do row reductions by hand until they're routine, and keep a picture in mind of what each matrix does to space. Review definitions like span, basis and rank often, because proofs and true-or-false questions depend on stating them exactly.

  1. Build intuition firstTutor chat

    Ask Kuest what span, a basis or an eigenvector means geometrically before you memorize the procedure.

  2. See transformations on the boardTeaching board

    Use the teaching board to draw how a matrix moves the plane, so determinants and eigenvectors have a picture.

  3. Work your problem setsSnap a photo

    Snap a row reduction or eigenvalue problem and work it step by step, checking each row operation.

  4. Memorize the definitionsFlashcards

    Turn definitions and the invertible matrix theorem into flashcards with spaced review.

  5. Drill true-or-false and computationQuizzes

    Take quizzes that mix computations with conceptual true-or-false questions, the way many linear algebra exams do.

  6. Take a mock midtermMock exams

    Upload your syllabus or notes and take a timed mock exam before each midterm and the final.

What you'll cover

Tap a topic to learn it now.

  1. 01Systems of linear equationsWrite a system as an augmented matrix and solve it by row reduction to echelon form.
  2. 02Vectors, linear combinations and spanAdd and scale vectors and decide whether a vector lies in the span of others.
  3. 03Linear independenceTest whether a set of vectors is independent and explain what dependence means.
  4. 04Matrix operations and inversesMultiply matrices, find inverses and use the invertible matrix theorem.
  5. 05Linear transformationsFind the matrix of a transformation and describe rotations, reflections and projections.
  6. 06DeterminantsCompute determinants by cofactors or row reduction and read them as area and volume scaling.
  7. 07Vector spaces and subspacesFind bases for the null space and column space and relate rank and dimension.
  8. 08Eigenvalues and eigenvectorsSolve the characteristic equation and find the eigenvectors for each eigenvalue.
  9. 09DiagonalizationWrite A = PDP⁻¹ when possible and use it to compute matrix powers.
  10. 10Orthogonality and least squaresProject onto subspaces, use Gram–Schmidt and fit a least-squares line.

Try asking

Tap a question and Kuest starts teaching it, step by step.

Helps you prepare for

  • College Linear Algebra
  • Linear Algebra and Differential Equations
  • Applied linear algebra for engineering and data science

A month of Kuest costs less than one hour with a tutor

Same patience, any hour, every subject. Or stay on the free plan for good.

Private tutor

$40–80for one hour

  • Booked days in advance
  • One subject per session
  • Stops when the hour ends

Kuest Plus

$10a month, billed yearly

  • Every subject and exam on this site
  • Any hour, as long as you need
  • Quizzes, flashcards, podcasts and mock exams

Study on any device

Phone, tablet or laptop. Your chats, plans and flashcards come with you.

Download on theApp StoreGet it onGoogle Play

Questions, answered

Your next study session starts here

Free forever plan. No card needed.

Start free