Includes index.

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.Features - More than 25% of the exercises are new or updated, especially computational exercises. Linear transformations form a “thread” that is woven into the fabric of the text. Their use enhances the geometric flavor of the text. A modern view of matrix multiplication is presented, with definitions and proofs focusing on the columns of a matrix rather than on the matrix entries. Focus on visualization: Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea. Numerical Notes provide a realistic slant to the text. Students are reminded frequently of issues that arise in real-life applications of linear algebra. Applications are varied and relevant. Each chapter opens with an introductory vignette that sets the state for some applications of linear algebra and provides a motivation for developing the mathematics that follows. Exercise sets are meticulously constructed and consist of the following elements. Each section features an abundant supply of exercises, ranging from routine computations to conceptual questions to applications. Innovative questions pinpoint conceptual difficulties that the authors have found in student papers over the years.