Álgebra Lineal

Course description

Álgebra Lineal is an undergraduate course offered to students in Mathematics, Industrial Engineering, and Systems Engineering. According to the official analytical plan, the course provides a mathematical language to model and solve multivariate problems arising in science and engineering, with applications to optimization, statistics, and computer science.

The general objective of the course is to represent and solve problem situations through multivariate linear systems, enabling planning, interpretation, and solution of problems in diverse areas of knowledge.

Main topics

• Systems of linear equations (2×2 and 3×3) and their geometric interpretation
• Gaussian and Gauss–Jordan elimination; homogeneous systems
• Matrix operations, classification of matrices, transpose, and LU factorization
• Determinants, adjoint matrix, inverse matrix, and Cramer’s rule
• Eigenvalues and eigenvectors and their applications
• Vector spaces, subspaces, linear combinations, span, and linear independence
• Orthonormal bases and Gram–Schmidt orthogonalization
• Vectors in the plane and space, dot and cross products, projections, lines, and planes