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Carroll, Ann K. Ebert Ricky W. Beatty, Susan S. Later, generalizations of these concepts appear as natural extensions of familiar ideas. Their use enhances the geometric flavor of the text. In Chapter 1, for instance, linear transformations provide a dynamic and graphical view of matrix-vector multiplication. Eigenvalues appear fairly early , in Chapters 5 and 7. Because this material is spread over several weeks, students have more time to absorb and to review these critical concepts.
Eigenvalues are motivated by and applied to discrete and continuous dynamical systems. Focus on visualization of concepts throughout — Each major concept in the course is given a geometric interpretation, as many students learn more effectively when they can visualize an idea. NEW - Modernized applications — After discussion with high-tech industry contacts and colleagues in applied areas, the authors have added new topics, vignettes, and applications to highlight for students and faculty the linear algebraic foundational material for machine learning, artificial intelligence, data science, and digital signal processing.
Projects can be used individually or in groups. Topics encompass a wide range of themes, from using linear transformations to create art to exploring additional ideas in mathematics. Applications are varied and relevant. Some applications appear in their own sections; others are treated within examples and exercises.
Each chapter opens with an introductory vignette that sets the stage for some applications of linear algebra and provides a motivation for developing the mathematics that follows. NEW - Added topics and applications prepare students with some of the foundations for machine learning, artificial intelligence, data analysis, and digital signal processing.
Numerical Notes provide a realistic slant to the text. Students are reminded frequently of issues that arise in real-life applications of linear algebra. Meticulously constructed exercise sets — 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.
A few carefully selected Practice Problems appear just before each exercise set. Complete solutions follow the exercise set. Conceptual Practice Problems and their solutions in most sections provide proof- or concept-based examples for students to review.
New to This Edition. Reach every student with MyLab Math Free-response writing exercises have been added to MyLab Math, allowing faculty to ask more sophisticated questions online and create a paperless class without losing the richness of discussing how concepts relate to each other and introductory proof writing.
This allows faculty and students to interact with figures and examples on a wider variety of electronic, devices, without the need to install the CDF player. PowerPoint lecture slides have been updated to cover all sections of the text and cover them more thoroughly. Table of Contents 1. Uniqueness of the Reduced Echelon Form B. Complex Numbers. Share a link to All Resources.
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