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

### Schedule

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)

### Homework

- due 09/06 [pdf] [tex] [solutions]
- due 09/13 [pdf] [tex] [solutions]
- due 09/20 [pdf] [tex] [solutions]
- due 09/27 [pdf] [tex] [solutions]
- due 10/04 [pdf] [tex] part preparation for midterm 1 [solutions]

### Handouts

- Functions [pdf]