7-61Use 7 8 5 =6-3-687-6871and 675=06-617-61-2 0 7 0= 27 8 587 1767 567 8 506-3-66-3-606-6=2])-7(0in the cofactor expansion of the matrix given, to find its determinant.

The answer is given below.Explanation:

Answered: 7-6 1 Use 7 8 5 = 6-3-6 87-6 8 7 1 and…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 7E

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Similar questions

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
Compute the determinants in Exercises 1-6 using cofactor expansion along the first row and along the first column. 2.
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 16 using the method of expansion by cofactors. Use a the third row and b the first column. 16. [342631478]
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]
Guided Proof Prove that the determinant of an invertible matrix A is equal to 1 when all of the entries of A and A1 is integers. Getting Started: Denote det(A) as x and det(A1) as y. Note that x and y are real numbers. To prove that det(A) is equal to 1, you must show that both x and y are integers such that their product xy is equal to 1. (i) Use the property for the determinant of a matrix product to show that xy=1. (ii) Use the definition of a determinant and the fact that the entries of A and A1 are integers to show that both x=det(A) and y=det(A1) are integers. (iii) Conclude that x=det(A) must be either 1 or 1 because these are the only integer solutions to the equation xy=1
Compute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. [522112300]
Find the determinant of the matrix. [4032013501511103]
Compute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. [0a0bcd0e0]

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7-6 1 Use 7 8 5 = 6-3-6 87-6 8 7 1 and 6 7 5 = 0 6 -6 1 7-6 1 -2 0 7 0 = 27 8 5 87 1 767 5 67 8 5 06-3-6 6-3-6 06-6 = 2 ])-7(0 in the cofactor expansion of the matrix given, to find its determinant.