handwritten9 and 10 Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a) diagonal method and(b) cofactor method.[1 5 66. F = |7 1 34 0 6-6 -3 -59-79. J=21-54-7957-74 37. G =1 7-7 4 90 a 0b b? b3 b40 c3 00 d? d³ 0a10. K =a a? a³8. H= |b b² b³[c c? c³

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Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.4: Determinants And Cramer's Rule

Problem 40E

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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.
Find the determinant of the matrix. [4032013501511103]
TEST Only one of the following matrix has an inverse. Find the determinant of each matrix, and use the determinant to identify the one that has an inverse. Then find the inverse. A=[141020101] B=[140020301]
Solve using Cramer’s rule. 415. Evaluate the determinant by expanding by minors: |322214103|
The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six triple products. Show that the determinant of a 44 matrix involves 24 quadruple products.
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]

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Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a) diagonal method and (b) cofactor method. [1 5 6 6. F = |7 1 3 4 0 6 -6 -3 -5 9 -7 2 1 9. J = -5 4 -7 5 7 -7