This text offers the most geometric presentation now available, emphasizes linear transformations as a unifying theme, and is recognized for its extensive and thought-provoking problem sets. While preserving the same table of contents as the previous edition, this revision is the outcome of a careful reflection (and appropriate change) on the wording of each idea. CONTENTS:1. Systems of Linear Equations. 2. Linear Transformations. 3. Subspaces of Rn and Their Dimension. 4. Linear Spaces. 5. Orthogonality and Least Squares. 6. Determinants. 7. Eigenvalues and Eigenvectors. 8. Symmetric Matrices and Quadratic Forms. 9. Linear Differential Equations.