Introduction to Linear Algebra

Undergraduate

Systems of linear equations, matrices, vectors, row reduction and echelon forms, linear independence and span, linear transformations, matrix operations, Invertible Matrix Theorem, elementary matrices, LU Decomposition, subspaces, determinants and multilinear functions, Cramer's Rule, eigenvalues and eigenvectors, geometry of vector spaces, Singular Value Decomposition if time permits; a proof-based approach, with applications. Prerequisite Mathematics 11 and 12, or Precalculus 11 and 12, or MATH 1003. Antirequisite(s): MATH 1323.