This is an introductory course in linear algebra, one of the most important and basic areas of mathematics, with many real-life applications. Students will be introduced to both the theory of vector spaces and linear transformations. They will learn row-reduction of matrices and diagonalization techniques which can be applied to problems in engineering, economics, finance, and computational biology.

The course will consist of a mixture of video lectures and tutorials, solving problems, weekly assignments, and class discussions.

Course Highlights:

• Points, vectors, and length
• Dot product, projection, angle, cross product, lines, and planes
• Gaussian elimination, linear combinations, linear dependence/independence, the kernel of matrix
• Adding and scaling matrices, types of square matrices, matrix multiplication, identity and inverse, applications of matrix algebra
• Determinants, area, linear maps, image, the solutions set for AX=B
• Introduction to vector spaces, subspaces, linear span and generators, bases, and coordinate vectors
• Building basis, rank, building linear maps, change of basis, similar matrices
• Determinants and their properties, determinants as area and volume, eigenvalues, and eigenvectors

Course Benefits:

• Solve systems of equations using Gauss-Jordan elimination
• Compute the determinant of a 2x2 and 3x3 matrix and find the inverse of a matrix
• Use axioms to define and prove vector spaces and subspaces
• Understand the relationship between a linear transformation and its matrix representation
• Find the eigenvalues and eigenvectors of a matrix and define them geometrically
• Compute the orthogonal projection of a vector onto a subspace given a basis for the subspace
• Understand applications of linear algebra and compute symbolic and graphical solutions using MatLab

Course Typically Offered: Online during Summer and Winter quarters.

Software: Students can use Free Online OCTAVE version for the purpose of this course or download the MATLAB and Simulink Student Suite software from MathWorks. Please note that there is a cost of \$99 associated with this version.

Prerequisites:  Before taking this course, students should have taken introduction to college algebra, or an equivalent course.