🕹️ Practice arcade
Extra games, not extra homework — timed sprints, survival runs that end when your lives run out, and mastery drills built from the same skills Linear Algebra — Vectors, Matrices, and the Geometry of Data teaches.
⚡ Sprints
Beat the clock.
🧮 Row-Reduction Rally
Set up the augmented matrix, run the row operation, read off the solution — as many as you can.
➡️ Vector Basics Blitz
Dot products, sums, scalar multiples, unit vectors — the arithmetic that has to become automatic.
🎲 Determinant Dash
$2\times2$, $3\times3$, by cofactors, by elimination — compute determinants every which way, fast.
✖️ Matrix Multiplication Mayhem
Row-times-column, matrix times vector, powers, composition — multiply matrices until it's second nature.
🔄 Linear Transformations Sprint
Build the standard matrix, apply it, name the geometry — scaling, shear, rotation, reflection.
📐 Lines and Planes Sprint
Parametrize a line, write a plane's equation, measure distances — the geometry of $\mathbb{R}^3$, quickly.
🌐 Markov & Graphs Sprint
One-step transitions, link matrices, walk counts — matrices as models of real networks.
📐 Norms & Orthonormal Family Sprint
A rectangular pulse's $L^1$ or $L^2$ norm, or a scaled family member's own norm on $[-\pi,\pi]$ -- three faces of "how big is this function."
💀 Survival
Each miss costs a life — lose them all and the run ends.
💀 Eigenvalue Survival
Characteristic equation, eigenvector check, triangular shortcuts, complex roots — one mistake ends it.
⚠️ Invertibility Survival
Invertible or singular? One wrong call and the run is over — how far can you get?
🧨 Subspace Survival
Is it a subspace? Are the vectors independent? One slip and the streak is gone.
🎯 Mastery
No clock — just get N in a row.
🎯 Diagonalization Mastery
Decide diagonalizability, build $P$ and $D$, use them to shortcut a power — five clean runs in a row.
⚖️ Weighted Inner Product Mastery
Compute a weighted dot product, then judge whether the weights still give a valid inner product — five in a row, no clock.
🧭 Orthogonality & Projection Mastery
Project onto a line, onto a subspace, decompose the residual — five in a row, no clock.
📉 Least-Squares Mastery
Normal equations, QR back-substitution, $R^2$ — fit the line and judge the fit, five times running.
🕸️ Four Subspaces Mastery
Column space, null space, row space, left null space — from one RREF, five times over.
🔁 Change-of-Basis Mastery
Coordinates relative to a basis, to standard, basis-to-basis — five conversions in a row, no clock.