Math 2135 Fall 2024

MATH 2135: Linear Algebra for Math Majors (Fall 2024)

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

08/26: some applications of linear algebra
08/28: systems of linear equations, matrix representation (1.1), matrix times vector
08/30: elementary row operations, row reduction, (reduced) echelon form (1.2)
09/04: free variables, solution in parametrized form, homogenous and inhomogenous systems
09/06: existence and number of solutions of Ax=b (1.2), vectors, linear combinations, span (1.3)
09/09: Ax=b is consisten iff b is in the span of the columns of A
09/11: solutions of homogenous and inhomogenous systems (1.5), nullspace of A
09/13: linear independent vectors (1.7)
09/16: linear transformations (1.8)
09/18: standard matrix of a linear transformation, every linear map is of the form x -> Ax (1.9)
09/20: characterizing injective, surjective x -> Ax by the columns of A (1.9)
09/23: matrix addition, composition of linear maps, matrix multiplication (2.1)
09/25: properties of matrix operations (2.1)
09/27: inverse matrix (2.2)
09/30: REVIEW [pdf]
10/02: MIDTERM 1
10/04: computing inverse matrix by row reduction (2.2)