MATH 164

Systems of linear equations over the real numbers. Vector algebra on ordered n-tuples (Euclidean n-space). Representation of linear systems as rectangular matrices. Elementary row operations; the row canonical form of a matrix. Basic matrix algebra (addition, subtraction, scalar multiplication). Matrix-vector multiplication; linear maps between Euclidean spaces. Matrix multiplication, square matrices, algorithms for matrix inverses. Introduction to determinants, eigenvalues, eigenvectors, and applications. Numerical linear algebra with computer algebra systems. Applications of linear algebra to other disciplines.