8. Determinants••Prove that the determinant of a triangular matrix is the product of its diagonal entries.Show that det(AB) = det(A)det(B) for any two square matrices A and B.

###(i)To prove that the determinant of a triangular matrix is the product of its diagonal entries,…

Answered: 8. Determinants • • Prove that the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 48RE

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Similar questions

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
Find the determinant of the matrix. [4032013501511103]
Explain the difference between a square matrix and its determinant. Give an example of each.
Solve using Cramer’s rule. 415. Evaluate the determinant by expanding by minors: |322214103|
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]
Evaluate the determinant |324012231| , by expanding by minors along the first row.
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.
Explain how to find the determinant of a 22 matrix.
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.
Compute the determinants in Exercises 7-15 using cofactor expansion along any row or column that seems convenient. 11.

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8. Determinants • • Prove that the determinant of a triangular matrix is the product of its diagonal entries. Show that det(AB) = det(A)det(B) for any two square matrices A and B.