Assuming that all matrices are n x n and invertible, solve for D. CABT DACTB = CAT.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Assuming that all matrices are n x n and invertible, solve for D.
CABT DACTB = CAT.
-1
D = A¯¹B¹CB¯¹ (C¹)¯¹B¯
d = (A¹)¯'ac²b(A¹)¯¹C-¹
-1
-1
-1
D = (B¹)¯¹A¯¹A¹B¯¹ (C²)¯`¹ A¯¹
D = (C²) ¹B-¹ATB-¹ (CT)-¹ A-¹
BTA-¹C-¹B-¹CTA-1
OD
=
-1
Transcribed Image Text:Assuming that all matrices are n x n and invertible, solve for D. CABT DACTB = CAT. -1 D = A¯¹B¹CB¯¹ (C¹)¯¹B¯ d = (A¹)¯'ac²b(A¹)¯¹C-¹ -1 -1 -1 D = (B¹)¯¹A¯¹A¹B¯¹ (C²)¯`¹ A¯¹ D = (C²) ¹B-¹ATB-¹ (CT)-¹ A-¹ BTA-¹C-¹B-¹CTA-1 OD = -1
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