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Using Matrix [A] prove that the Property 1 and 2 of determinant are true.

Using Matrix [A] prove that the Property 1 and 2 of determinant are true.

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter8: Engineering Materials
Section: Chapter Questions
Problem 85CQ
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a.Using Matrix [A] prove that the Property 1 and 2 of determinant are true.

 

[2 -5 -6 A = 5 7 -1 l8 -9 2
Transcribed Image Text:[2 -5 -6 A = 5 7 -1 l8 -9 2
1. Determinant of a Transpose The determinant of a transpose AT of A is equal to the determinant of A. det(AT) = det(A) 2. Interchange of Rows and Columns The determinant changes its sign if two adjacent rows (or columns) are interchanged. a12 |a11 ain |a21 а22 a2n a21 а22 a2n a11 a12 ain ... ... ... |an1 an2 ann |an1 an2 ann ... ....
Transcribed Image Text:1. Determinant of a Transpose The determinant of a transpose AT of A is equal to the determinant of A. det(AT) = det(A) 2. Interchange of Rows and Columns The determinant changes its sign if two adjacent rows (or columns) are interchanged. a12 |a11 ain |a21 а22 a2n a21 а22 a2n a11 a12 ain ... ... ... |an1 an2 ann |an1 an2 ann ... ....
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