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With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. Table of Contents Chapter 1 Linear Equations in Linear Algebra Chapter 2 Matrix Algebra Chapter 3 Determinants Chapter 4 Vector Spaces Chapter 5 Eigenvalues and Eigenvectors Chapter 6 Orthogonality and Least Squares Chapter 7 Symmetric Matrices and Quadratic Forms Chapter 8 The Geometry of Vector Spaces