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Linear Algebra

A Visual and Application-Driven Approach for High School Students

Sanjay Dagam  ·  2026

215 pages 9 Chapters Solutions Manual included Prerequisite: AP Calculus High School / Early College
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215
Pages · Main Text
213
Pages · Solutions
9
Chapters
3×
Difficulty levels

Built for students who want to understand, not just compute.

This textbook takes a visual, application-driven approach to linear algebra—designed specifically for high school students who've completed AP Calculus and are ready to explore one of the most powerful branches of mathematics.

Every chapter connects abstract ideas to real-world applications: from Google's PageRank algorithm to Pixar's animation pipeline, from quantum mechanics to machine learning.

📘
Definition & theorem boxes
Key results highlighted with color-coded callouts for quick reference and review.
✏️
Three difficulty levels
Basic, Intermediate, and Challenge problems in every chapter with full solutions.
🌐
Real-world applications
Each chapter closes with a section connecting theory to engineering, CS, and science.
🔬
Proofs included
Mathematical reasoning presented clearly — not skipped — to build genuine understanding.

Contents

9 chapters
1
Chapter 01
Introduction to Vectors
Notation, operations, dot & cross products, applications
2
Chapter 02
Systems of Linear Equations
Gaussian elimination, row echelon form, applications
3
Chapter 03
Matrices
Operations, transpose, inverse, Markov chains, cryptography
4
Chapter 04
Determinants
Cofactor expansion, Cramer's rule, volume, eigenvalue preview
5
Chapter 05
Vector Spaces
Subspaces, basis, dimension, linear independence
6
Chapter 06
Eigenvalues & Eigenvectors
Characteristic polynomial, diagonalization, PageRank
7
Chapter 07
Linear Transformations
Kernel, range, matrix representations, applications
8
Chapter 08
Inner Product Spaces
Inner products, norm, Cauchy-Schwarz inequality, orthogonality
9
Chapter 09
Applications & Advanced Topics
Markov chains, PageRank, linear programming
Textbook
Solutions Manual
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