Practice
Practice Arena
Endless exercises with instant feedback, worked solutions, XP, streaks, sprints and badges.
Scalar
0 XP · 100 XP to Vector
- First stepsSolve your first practice exercise.
- On a roll5 correct answers in a row in one topic.
- Unstoppable10 correct answers in a row in one topic.
- All-rounderSolve at least one exercise in every topic.
- MasterEarn all three mastery stars in a topic.
- SprinterAnswer 8 or more correctly in a 60-second sprint.
- HabitPractise on 3 days in a row.
- Echelon expertRow-reduce a matrix to reduced row echelon form.
- Under parSolve a Gauss-Jordan challenge within par.
- Right angleFind two orthogonal non-zero vectors in the 3D tool.
- TransformerWatch a matrix transform space in the 3D tool.
- Order mattersDiscover that AB ≠ BA in the matrix multiplication tab.
- InverterCompute an inverse and confirm that A·A⁻¹ = E.
- DecomposerWork through an LU decomposition all the way to the solution x.
- PredictorPredict every multiplier of an LU decomposition in quiz mode.
- FlatlandFind a matrix that squashes space flat (det A = 0).
Choose a topic
Correct answers earn XP. Exercises get harder as you master a topic.
- ☆☆☆
Vector addition
a + b and a − b, component by component.
Not started yet
- ☆☆☆
Linear combinations
λ·a, λ·a + μ·b
Not started yet
- ☆☆☆
Dot product
a • b — and spotting orthogonal vectors.
Not started yet
- ☆☆☆
Length of a vector
|a| = √(a • a)
Not started yet
- ☆☆☆
Matrix addition
A + B, A − B and λ·A.
Not started yet
- ☆☆☆
Matrix × vector
Ax, row by row.
Not started yet
- ☆☆☆
Determinant
2×2 and 3×3 determinants.
Not started yet
- ☆☆☆
Linear systems
Solve Ax = b.
Not started yet
- ☆☆☆
Matrix multiplication
AB: row of A times column of B.
Not started yet
- ☆☆☆
Transpose
Aᵀ: rows become columns.
Not started yet
- ☆☆☆
Inverse matrix
A⁻¹ with A·A⁻¹ = E.
Not started yet
- ☆☆☆
LU decomposition
Find L or U with A = LU.
Not started yet