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

Syllabus

Schedule

1. 08/21: some applications of linear algebra
2. 08/24: systems of linear equations, matrix representation (1.1), matrix times vector
3. 08/26: elementary row operations, row reduction, (reduced) echelon form (1.2)
4. 08/28: free variables, solution in parametrized form, homogenous and inhomogenous systems
5. 08/31: existence and number of solutions of Ax=b (1.2), vectors
6. 09/02: linear combinations, span (1.3),
7. 09/04: Ax=b is consistent iff b is in the span of the columns of A
8. 09/09: solutions of homogenous and inhomogenous systems (1.5), nullspace of A
9. 09/11: linear independent vectors (1.7)
10. 09/14: characterizing linear dependent vectors (1.7), linear transformations (1.8)
11. 09/16: standard matrix of a linear transformation
12. 09/18: every linear map is of the form x -> Ax (1.9)
13. 09/21: review of injective, surjective maps
14. 09/23: characterizing injective, surjective x -> Ax by the columns of A (1.9)
15. 09/25: matrix addition, composition of linear maps, matrix multiplication (2.1), REVIEW [pdf], [practice midterm], [solutions]
16. 09/28: MIDTERM 1
17. 09/30: properties of matrix operations (2.1),
18. 10/02: inverse matrix, transpose (2.2)
19. 10/05: computing inverse matrix by row reduction (2.2)
20. 10/07: characterizing invertible matrices (2.3)
21. 10/09: computations in Mathematica [available from CU to download and install] [Mathematica notebook]
22. 10/12 axioms of vectors spaces and examples: tuples, matrices, sequences, functions as vector spaces (4.1), subspaces (2.8, 4.1)
23. 10/14: spans are subspaces, basis of subspaces, basis of null space (2.8, 4.3)

Homework

1. due 09/04 [pdf] [solutions]
2. due 09/11 [pdf] [solutions]
3. due 09/18 [pdf] [solutions]
4. due 09/25 [pdf] [solutions]
5. due 10/02 [pdf] [solutions]
6. due 10/09 [pdf] [solutions]
7. due 10/16 [pdf]