Linear Algebra — Contents
Linear systems, matrices, determinants, vectors, vector spaces, linear transformations, eigenvalues and orthogonality — with interactive labs, full solutions and bilingual terms.
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Welcome to Linear Algebra — the mathematics of vectors, matrices and linear maps that sits underneath computer graphics, data science, engineering, economics and quantum physics. Every section has worked examples with step-by-step solutions, live labs where you drag vectors and watch matrices transform the plane, full solutions to every exercise and a self-check quiz.
🎮 Interactive labsDrag vectors, step through row reduction, and watch a matrix stretch, shear and rotate the plane — eigenvectors stay on their own line.
✅ Every problem solvedEvery example and exercise comes with a step-by-step solution to reveal when you are ready.
ع Bilingual termsHover a dotted word for its Arabic name and meaning, or press ع to show Arabic terms throughout.
🔬 Research tasksEach section ends with an optional mini-investigation that connects the mathematics to real data.
Contents
🔑 Access
Chapter 1 is free; Chapters 2–4 🔒 need a Basic or Premium plan; Chapters 5–8 👑 are for Premium members. To get access, subscribe and contact admin@tutorda.org. The welcome page, formula sheet and glossary are open to everyone.
Chapter 1 · Free
Systems of Linear Equations
Chapter 2 · 🔒 Basic
Matrices
Chapter 3 · 🔒 Basic
Determinants
Chapter 4 · 🔒 Basic
Vectors in ℝⁿ
Chapter 5 · 👑 Premium
Vector Spaces
Chapter 6 · 👑 Premium
Linear Transformations
Chapter 7 · 👑 Premium
Eigenvalues and Eigenvectors
Chapter 8 · 👑 Premium
Orthogonality and Least Squares
📚 About this book
8 chapters, 29 sections. Published by D'Math University on TutorDA. Prerequisite: school algebra — solving equations, working with fractions, and coordinates in the plane. No calculus is needed except in a few clearly marked applications.