Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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![EXERCISE 4.4.2: Proving that the determinant of a matrix and the transpose of the matrix are equal.
Prove.
(a) If A is an n x n matrix then det A = det AT](https://content.bartleby.com/qna-images/question/c167378a-6772-4355-bdb0-a5fec1af8d0e/2836d0a7-40a0-48a0-9bc8-fc1db0db33e0/r9uzmea_thumbnail.jpeg)
Transcribed Image Text:EXERCISE 4.4.2: Proving that the determinant of a matrix and the transpose of the matrix are equal.
Prove.
(a) If A is an n x n matrix then det A = det AT
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- 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]arrow_forwardFind 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]arrow_forwardLet A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.arrow_forward
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