(a) If A and C arenxn matrices with C invertible, prove that: det (C-AC) = det(A). (b) Given that det(A) = -1 and det(C) = 2, compute the following: (i) det(AC) (ii) det(A") (ii) det(C-AC)
(a) If A and C arenxn matrices with C invertible, prove that: det (C-AC) = det(A). (b) Given that det(A) = -1 and det(C) = 2, compute the following: (i) det(AC) (ii) det(A") (ii) det(C-AC)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![(a)
If A and C are nx n matrices with C invertible, prove that:
det (C-AC) = det(A).
(b)
Given that det(A) = -1 and det(C) = 2, compute the following:
(i)
det(AC)
(ii)
det(A")
(ii) det(C-'AC)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F119bf395-4fd3-4679-8690-a631539097d2%2F61d407e9-34eb-41f9-a592-4cdd624d25a7%2F54xn9p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a)
If A and C are nx n matrices with C invertible, prove that:
det (C-AC) = det(A).
(b)
Given that det(A) = -1 and det(C) = 2, compute the following:
(i)
det(AC)
(ii)
det(A")
(ii) det(C-'AC)
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