Course 10 · College

Linear Algebra

The language of modern mathematics, data science, and engineering.

Overview

What this course covers.

Linear Algebra is one of the most broadly applicable courses in mathematics. From solving systems of equations to machine learning and computer graphics, the tools developed here — matrices, vector spaces, eigenvalues — appear everywhere. This course builds both computational skill and theoretical understanding.

PrerequisitesCalculus II (AP Calculus BC) or concurrent enrollment.

Curriculum

Topics & units.

Unit 1

Systems & Matrices

›Systems of linear equations
›Row reduction & echelon form
›Matrix operations
›Inverse matrices & LU factorization

Unit 2

Determinants

›Cofactor expansion
›Properties of determinants
›Cramer's rule
›Geometric interpretation (area/volume)

Unit 3

Vector Spaces

›Vector spaces and subspaces
›Null space, column space, row space
›Linear independence and bases
›Dimension and rank

Unit 4

Eigenvalues & Applications

›Eigenvalues and eigenvectors
›Diagonalization
›Orthogonality and least squares
›Applications: Markov chains, SVD (intro)

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