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The cornerstone of ELEMENTARY LINEAR ALGEBRA is the author's clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Featuring a new design that highlights the relevance of the mathematics and improves readability for students, the Eighth Edition also incorporates conceptual Capstone exercises that reinforce multiple concepts in each section. Data and applications reflect current statistics and examples to engage students and demonstrate the link between theory and practice. WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in your hands, enabling you to deploy assignments, add your own content, instantly assess individual student and class performance, and and help your students master course concepts.
- A new, more student-friendly design includes a greater number of images that make content more relevant for students.
- A new section has been added to chapter 2. Section 2.5, Markov Chains, was added to explore the topic of Markov Chains in greater depth.
- A new companion website, LarsonLinearAlgebra.com, developed by Ron Larson, offers students free access to multiple learning tools and resources. Your students can explore examples, watch lesson videos, download data sets, and much more.
- New interactive examples allow students to explore linear algebra by manipulating matrices and functions and observing the results.
- Pedagogical support--including self-assessment tools, review sections, and writing activities--allows students to check their understanding of each section and helps them develop critical thinking skills.
- WEBASSIGN: ELEMENTARY LINEAR ALGEBRA, Eight Edition, is the powerful online homework and course management system that engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.
- To motivate students by emphasizing the relevance of the content, each chapter opener contains a list of sections, five photos with references to applications, and an arrow indicating the section in which each application appears.
- Capstone exercises, each of which covers several concepts, are available in each section. Conceptual in nature, they reinforce key ideas learned in the section without being time-consuming or tedious for students.
- Learning objectives are available at the beginning of every section and online at the student website for quick reference and/or review.
- Guided Proofs help students successfully complete theoretical proofs by leading them, step-by-step, through the logical sequence of statements necessary to reach the correct conclusion.
Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations.
Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Markov Chains. Applications of Matrix Operations.
The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants.
4. VECTOR SPACES.
Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces.
5. INNER PRODUCT SPACES.
Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces.
6. LINEAR TRANSFORMATIONS.
Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations.
7. EIGENVALUES AND EIGENVECTORS.
Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors.
8. COMPLEX VECTOR SPACES (online).
Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre’s Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces.
9. LINEAR PROGRAMMING (online).
Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints.
10. NUMERICAL METHODS (online).
Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Instructor's Web Site with Solutions Manual for Larson's Elementary Linear Algebra, 8th
This time-saving manual provides complete solutions to all the problems in the text.
Everything you need for your course in one place! This collection of product-specific lecture and class tools is available online via the instructor resource center at www.cengage.com/login. You'll be able to access and download materials such as PowerPoint presentations, images, instructor’s manual, videos, and more.
Cengage Learning Testing, powered by Cognero® Instant Access
Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to: import, edit, and manipulate content from the text's test bank or elsewhere, including your own favorite test questions; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want.
Student Solutions Manual
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Instructor Sample/Review copy of Larson's Elementary Linear Algebra, 8th.
Student Solutions Manual
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.