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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 should 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.

More information: For more information about this course contact unex-techdata@ucsd.edu.

Course Number: MATH-40023
Credit: 4.00 unit(s)

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