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.