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Linear algebra 1

Build vectors and 2×2 matrices and watch them act on a grid — a linear map, seen as a picture, is what makes the algebra behind graphics, games and machine learning make sense.

Briefing

Everything happens on a grid you can see. You drag arrows, stretch and spin the whole plane, and watch a 2x2 table of numbers do it — so that by the end a matrix is a picture you can read, not a rule you memorised.

You'll learn to

  • Add and scale vectors, and build any point from two basic ones
  • Read what a matrix does straight from its two columns
  • Build a matrix that produces a transformation you want
  • Use the determinant as the area it scales by, and see why order matters
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Start: Vectors are arrows
Before you work with matricesOptional warm-upStarts from zero: directions on a map, arrows you can add and stretch, and rules that move every point. Ten minutes.

  1. Vectors are arrows

    Up next

    Adding them is tip to tail

  2. Scaling

    One number, one vector, a whole line

  3. Finding a and b

    Two directions, two equations, one method

  4. Linear combinations

    Two vectors can reach anywhere

  5. Matrices move space

    The columns say where the grid lands

  6. Build the transform

    Set the columns, watch the shape follow

  7. The determinant is area

    One number tells you how much bigger

  8. Order matters

    A·B is not the same as B·A

  9. Where this shows up

    Graphics, games, and machine learning