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The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' 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 Seventh Edition also incorporates new 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. Cengage Learning's Enhanced WebAssign®, which allows you to create online homework assignments that draw from thousands of the text's end-of-chapter questions, is available with the text.
- Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content to help them develop a deeper conceptual understanding of their subject matter. Students have access to an interactive eBook offering links to YouTube videos, video solutions, and more to bring the mathematics to life. You can build online assignments by selecting from thousands of text-specific problems, supplemented with problems from any Cengage Learning textbook.
- A new, more student-friendly design includes a greater number of images that make content more relevant for students. The trim size and font size in the exercise sets have been increased, making the text easier for students to read.
- 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.
- New Capstone exercises, each of which covers several concepts, have been added in each section. Conceptual in nature, they reinforce key ideas learned in the section without being time-consuming or tedious for students.
- Coverage of Computer Algebra Systems (CAS) includes an online technology guide. Appendix B--also available online--offers an introduction to MATLAB, Maple, Mathematica, and Graphing Calculators; a walkthrough of the keystrokes needed for select examples; an applications section; and "Technology Pitfalls" students may encounter in using their CAS.
- All real data in the exercises and examples has been updated to reflect current statistics and information. Many new exercises have been added to the text as well.
- 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.
- 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.
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. 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.