determinants of Matrices Finding the Determinants using Elementary Row OperationsE =2 1 3 110 1102100 1 2311-2 -7 012001F =•100039000ntoma321-1

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Answered: Finding the Determinants using…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Matrices And Determinants

Section6.4: Determinants And Cramer’s Rule

Problem 11E

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True or False ? a To find the determinant of a triangular matrix, add the entries on the main diagonal. b To find the determinant of a matrix, expand by cofactors in any row or column. c When expanding by cofactors, you need not evaluate the cofactors of zero entries.
True or False ? a The determinant of a 22 matrix A is a21a12a11a22. b The determinant of a matrix of order 1 is the entry of the matrix. c The ij-cofactor of a square matrix A is the matrix obtained by deleting the ith row and jth column of A
Find the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a the third row and b the first column. 16. [342631478]
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, detB = detA. 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.
Find the determinant of the matrix in Exercise 15 using the method of expansion by cofactors. Use a the second row and b the second column. 15. [321456231]
Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is O. For simplicity, use a 22 .

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Finding the Determinants using Elementary Row Operations E = 2 1 3 1 10 11 0210 0 1 23 1 1 -2 -7 0 1 2 001 F = •1000 39000 ntoma 321- 1