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Linear Algebra Lab

1.5 Credits | 300 Level | 15 Contact hours

Linear Algebra: Ideas and Applications. Richard C. Penney. John Wiley & Sons, Incorporated. Fourth Edition.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).

The course is structured in the following contents
1. Solving Linear Systems and General Matrix Operations
2. Matrix Algebra
3. Operations on Square Matrices
4. Linear Independence, Bases, and Matrix Inverse
5. Eigenvalues and Eigenvectors

Week Dates Sections Covered & Quiz Schedule Homework due dates
1 Jan 17 Solving Linear Systems HW #1

2 Jan 24 Matrix Form of Linear Systems HW #2

3 Jan 31 Gauss-Jordan Elimination HW #3

4 Feb 07 Applications HW #4

5 Feb 17 Matrix Algebra: Fundamental matrix structures HW #5

6 Feb 21 Matrix Algebra: Transpose and Structural Patterns HW #6

7 Feb 28 Addition and Multiplication of Matrices HW #7

8 Mar 07 Partial exam & review HW #8

9 Mar 14 Operations on Square Matrices and Determinants HW #9

10 Mar 21 Cramer’s Rule HW #10

11 Mar 28 Linear Independence, Bases, and Matrix Inverse HW #11

12 Apr 04 Matrix Inverse HW #12

13 Apr 18 Matrix Theory Review HW #13

14 Apr 25 Eigenvalues and Eigenvectors HW #14
15 May 02 Diagonalization of matrices HW #15
16 May 09 Final Exam & review

To provide the student with a good understanding of the following topics and their applications:
• Systems of linear equations
• Row reduction and echelon forms
• Matrix operations, including inverses
• Linear dependence and independence, bases and dimensions
• Determinants and their properties
• Cramer’s Rule
• Eigenvalues and eigenvectors. Diagonalization of a matrix

1. Attendance and in-class participation: 10%. Attendance is mandatory to obtain the credits.

2. Assignments: 10%. Students should deliver the proposed assignments periodically.

3. Assignments on lectures: 20%

4. Partial Exam: 30 %

5. Final Exam: 30 %

In the Spanish university system, courses are graded on a scale of 0 to 10 points, with the following qualitative equivalences:
0 - 4,9: "Suspenso" (Fail)
5 - 6,9: "Aprobado" (Pass)
7 - 8,9: "Notable" (Good)
9 - 10: "Sobresaliente" (Excellent)


To pass a course is necessary to get at least 5 points, but class attendance will also be considered, as it is shown below.