Overview
Mathematics 270: Linear Algebra I is suggested for students in the Science programs. The course covers systems of linear equations; matrices; inverse of a matrix; determinant; vectors in two, three, and n dimensions; Euclidean and general vector spaces; and applications of linear algebra.
Outline
Unit 1: Systems of Linear Equations and Matrices
Some of the topics covered in this unit are systems of linear equations, Gaussian and Gauss-Jordan elimination, matrices, their operations and their algebraic properties, and applications to traffic flow and chemical equations.
Unit 2: Inverse of a Matrix, Linear Systems, and Special Forms of Matrices
Some of the topics covered in this unit are inverse of a matrix and its properties, methods for finding the inverse, linear systems and the inverse of a matrix, special forms of matrices, and applications to economic systems.
Unit 3: Determinant of a Matrix
Some of the topics covered in this unit are the determinant with minors and cofactors, determinants by row reduction, properties of the determinant, equivalent statements theorem for an invertible matrix, Cramer’s rule, and applications to geometry.
Unit 4: Euclidean Vector Spaces in 2, 3, and n dimensions
Some of the topics covered in this unit are vector operations and properties, lengths, distances and dot/inner product, orthogonality, vector and parametric equations of lines and planes, cross product, eigenvalues and eigenvectors, applications to dynamical systems, and Markov chains.
Unit 5: General Vector Spaces
Some of the topics covered in this unit are real vector spaces, subspaces, linear independence, basis, dimension, introduction to linear transformations, basic matrix transformations, and applications to computer graphics.
Note: Each unit has a section with a linear algebra application.
Learning outcomes
Upon successful completion of this course, you should be able to
- solve systems of linear equations using different methods such as Gaussian and Gauss-Jordan elimination, coefficient matrix inversion, and Cramer’s rule.
- calculate basic matrix operations, inverses and determinants, and apply them to systems of linear equations and basic linear transformations.
- demonstrate understanding of the basic concepts within a vector space, including vectors, vector operations, inner and cross products, subspace, linear independence, span, basis, and dimension.
- find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial.
- use the concepts of matrices, system of linear equations, inverse matrix, determinant, and vector spaces to solve applied linear algebra problems.
Evaluation
To receive credit for MATH 270, you must achieve a course composite grade of at least D (50 percent) and a grade of at least 50 percent on the final assessment. The weighting of the composite grade is as follows:
| Activity | Weight |
| Assignments 1–5 (3% each) | 15% |
| Midterm assessment | 35% |
| Final assessment | 50% |
| Total | 100% |
Materials
Digital course materials
Links to the following course materials will be made available in the course:
Anton, H., & Rorres, C. (2014). Elementary linear algebra: Applications version (11th ed.). Wiley.
Anton, H., & Rorres, C. (2014). Student solutions manual: Elementary linear algebra and Elementary linear algebra: Applications version (11th ed.). Wiley.