This course introduces students to vectors, linear transformations, and matrices with applications to the geometry of Euclidean three-space and generalizations. The course usually begins with a careful study of the solution of linear systems of equations and ends with the orthogonal diagonalization of symmetric matrices. Topics include row reduction, determinants, bases, dimension, rank, nullity, eigenvalues, and eigenvectors. The course meets four times weekly with a faculty member in small sections. Only students who did very well in Calculus I should attempt this course before completing a full year of calculus.