← Math: Matrices

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Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

Matrices and operations on them, multiplication, the determinant and the inverse matrix, systems of equations (Cramer, Gauss), a matrix as a transformation: scaling, rotation, composition, homogeneous coordinates and 4×4 — a bridge to shaders. Grade 7–8 math is enough.

Course program: 26 lessons

Matrices and operations

  1. What a matrix is
  2. Addition and scalar multiplication
  3. Matrix operations: more
  4. Transpose
  5. Checkpoint: matrices and operations

Matrix multiplication

  1. Matrix times vector
  2. Matrix multiplication
  3. Matrix multiplication: more
  4. AB ≠ BA and the identity matrix
  5. Checkpoint: matrix multiplication

Determinant and inverse matrix

  1. 2×2 determinant
  2. What the determinant means: area
  3. 3×3 determinant
  4. Inverse matrix
  5. Inverse matrix: more
  6. Checkpoint: determinant and inverse matrix

Systems of linear equations

  1. A system as A·x = b
  2. Cramer's rule
  3. Gaussian elimination
  4. Checkpoint: systems of equations

A matrix as a transformation

  1. Scaling and reflection
  2. Rotation
  3. Composition is a matrix product
  4. Homogeneous coordinates and translation
  5. 4×4 matrices and projection
  6. Checkpoint: transformations