Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 3.2, Problem 47E

Guided Proof Prove Property 2 of Theorem 3.3: When B is obtained from A by adding a multiple of a row of A to another row of A, det(B) = det(A). Getting Started: To prove that the determinant of B is equal to the determinant of A, you need to show that their respective cofactor expansions are equal.

(i) Begin by letting B be the matrix obtained by adding c times the jth row of A to the ith row of A.
(ii) Find the determinant of B by expanding in this ith row.
(iii) Distribute and then group the terms containing a coefficient of c and those not containing a coefficient of c.
(iv) Show that the sum of the terms not containing a coefficient of c is the determinant of A, and the sum of the terms containing a coefficient of c is equal to 0.
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Chapter 3 Solutions

Elementary Linear Algebra (MindTap Course List)

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Prob. 67CRCh. 3.CR - Prob. 68CRCh. 3.CR - Prob. 69CRCh. 3.CR - Prob. 70CRCh. 3.CR - Prob. 71CRCh. 3.CR - Prob. 72CRCh. 3.CR - Prob. 73CRCh. 3.CR - Health Care Expenditures The table shows annual...Ch. 3.CR - Prob. 75CRCh. 3.CR - Prob. 76CRCh. 3.CR - True or False? 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