2021-2023 Catalog

MATH 220 Linear Algebra

Introduces matrix theory. Topics covered include: systems of equations, Gaussian elimination, LU decomposition , Euclidean vector spaces and subspaces, linear transformations, basis sets and dimensions, span of a vector space, Gram-Schmidt orthogonalization, least squares methods, eigenvalues, eigenvectors,and matrix diagonalization. Focuses on key vocabulary and conceptual understanding of Linear Algebra. Real world applications are emphasized. Prerequisite: MATH 126 (QS)

Credits

5

Outcomes

  1. Perform matrix operations, calculate determinants, find inverses for matrices (where possible), and find the transpose of a matrix.
  2. Use elementary row operations to solve systems of linear equations using Gaussian Elimination and Gauss-Jordan reduction methods.
  3. Apply LU decomposition methods to factorize a matrix.
  4. Identify a system of linear equations as independent, inconsistent, or dependent.
  5. Identify properties of Euclidean vector spaces and the effects of linear transformations.
  6. Perform vector operations; use properties of vector operations; and determine vector subspaces, spanning sets, and bases of vector spaces.
  7. Determine whether a set of vectors forms the basis for a set and find the dimension of a subspace.
  8. Find inner products and a basis for a given inner product space.
  9. Use matrices to perform transformations between vector spaces.
  10. Find the kernel, range, rank, and nullity of a linear transformation.
  11. Use Gram-Schmidt orthogonalization to find orthonormal vectors.
  12. Apply QR decomposition methods to factorize a matrix.
  13. Find real eigenvalues and eigenvectors of a square matrix.
  14. Diagonalize symmetric matrices.
  15. Apply matrix algebra to data fitting and least squares analysis.
  16. Communicate mathematical ideas.
  17. Use appropriate technology strategically.