A first course on linear algebra in R^n emphasizing the interplay between algebraic and geometric perspectives. Topics include systems of equations, Gaussian elimination, representations of lines and planes, dot products, subspaces and translated subspaces, bases and change of basis, projections, the rank and nullity of a linear transformation, the rank/nullity/row space/column space of a matrix, matrix inverses, determinants, eigenvectors and eigenvalues, and matrix diagonalization. While not emphasizing proofs, this course does maintain a careful distinction between vectors and their representation in a basis as well as between matrices and linear transformations.