You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Cletis Bagle. Skip to content. Home About. Share this: Twitter Facebook. Like this: Like Loading Abundant computer exercises , more extensive than any other linear algebra book on the market, help students to visualize and discover linear algebra and allow them to explore more realistic applications that are too computationally intensive to work out by hand.
These exercises also provide students with experience in performing matrix computations. Worked out examples illustrate new concepts, making the material less abstract and helping students quickly build their understanding. Two chapter tests for every chapter help students study for exams and get the practice they need to master the material. New to This Edition. New applications added to Chapters 1, 5, 6, and 7 —in Chapter 1 Matrices and Systems of Equations , the authors introduce an important application to the field of Management Science.
Management decisions often involve making choices between a number of alternatives. The authors assume that the choices are to be made with a fixed goal in mind and should be based on a set of evaluation criteria. These decisions often involve a number of human judgments that may not always be completely consistent.
The analytic hierarchy process is a technique for rating the various alternatives based on a chart consisting of weighted criteria and ratings that measure how well each alternative satisfies each of the criteria. Chapter 1 Matrices and Systems of Equations , shows how to set up such a chart or decision tree for the process. After weights and ratings have been assigned to each entry in the chart, an overall ranking of the alternatives is calculated using simple matrix-vector operations.
Chapters 5 Orthogonality and 6 Eigenvalues revisit the application and discuss how to use advanced matrix techniques to determine appropriate weights and ratings for the decision process. Finally, Chapter 7 Numerical Linear Algebra presents a numerical algorithm for computing the weight vectors used in the decision process. New subsection in Chapter 3, Section 2 Subspaces —one important example of a subspace occurs when finding all solutions to a homogeneous system of linear equations.
This type of subspace is referred to as a nullspace. A new subsection has been added to show how the nullspace is also useful in finding the solution set to a nonhomogeneous linear system.
The subsection contains a new theorem and also a new figure that provides a geometric illustration of the theorem.
Three related problems have been added to the exercises at the end of Section 2. Chapter 7, Section 1 Floating-Point Numbers revised —Two subsections have been revised and modernized. The cookie is used to store the user consent for the cookies in the category "Other.
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Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. These cookies track visitors across websites and collect information to provide customized ads. This follows directly from Exercise 19 of Section 2.
If A is nonsingular then B is nonsingular, and conversely. Suppose B is singular. Then by Theorem 2. Theorem 2. Hence, B is nonsingular. If A has a row of zeros, then A cannot be row equivalent to In , and so by Corollary 2.
By Theorem 2. Suppose that A is nonsingular. We consider the case that A is nonsingular and upper triangular. A similar argument can be given for A lower triangular.
The elementary matrix Ei will be upper triangular since it is used to introduce zeros into the upper triangular part of A in the reduction process.
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