Math 2135 Fall 2026

MATH 2135: Linear Algebra for Math Majors (Fall 2026)

Numbers are for orientation and refer to sections in Lay et al, Linear algebra and its applications.

08/21: some applications of linear algebra
08/24: systems of linear equations, matrix representation (1.1), matrix times vector
08/26: elementary row operations, row reduction, (reduced) echelon form (1.2)
08/28: free variables, solution in parametrized form, homogenous and inhomogenous systems
08/31: existence and number of solutions of Ax=b (1.2), vectors
09/02: linear combinations, span (1.3),
09/04: Ax=b is consistent iff b is in the span of the columns of A
09/09: solutions of homogenous and inhomogenous systems (1.5), nullspace of A
09/11: linear independent vectors (1.7)
09/14: characterizing linear dependent vectors (1.7), linear transformations (1.8)
09/16: standard matrix of a linear transformation
09/18: every linear map is of the form x -> Ax (1.9)
09/21: characterizing injective, surjective x -> Ax by the columns of A (1.9)