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Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmanns

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 6.2.42 Chapter 6

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 6.2.42

Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmanns Identity: dim(U W) dimU dimW dim(U W) [Hint: The subspace U W is defined in Exercise 48of Section 6.1. Let B {v1,..., vk} be a basis forU W. Extend B to a basis C of U and a basis D of W.Prove that C D is a basis for U W.]

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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmanns