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(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
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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(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)
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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