### Linear Algebra

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

#### Transferring UC San Diego Division of Extended Studies Credit

Many UC San Diego Division of Extended Studies may qualify for college credit to UC San Diego or other colleges or universities. The transfer of credit is determined solely by the receiving institution. Please discuss how your individual courses will transfer with the registrar's office at the receiving institution before you enroll.

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.