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Cos sin 0 = Let A-s (a) (b) sin 0 со B = (1 − A)(I + A)−¹ and C = (I − B³)(I + B³)−1 Assume (I + A)−¹ = (I + A−¹)/ det(I + A). Show that BT = -B If (I + B³) and (I – B³) are both invertible and (I − B³)−¹(I + B³) = (I + B³)(I − B³)-¹. Show that C is orthogonal. (Hint: reduce CT to C-1 by using (a))

Cos sin 0 = Let A-s (a) (b) sin 0 со B = (1 − A)(I + A)−¹ and C = (I − B³)(I + B³)−1 Assume (I + A)−¹ = (I + A−¹)/ det(I + A). Show that BT = -B If (I + B³) and (I – B³) are both invertible and (I − B³)−¹(I + B³) = (I + B³)(I − B³)-¹. Show that C is orthogonal. (Hint: reduce CT to C-1 by using (a))

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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Let A = [Cine (a) (b) sin Ꮎ nº], B = (1 − A)(I + A)−¹ and C = (I − B³) (I + B³)−1 -1 COS Assume (I + A)-¹ = (1 + A−¹)/ det(I + A). Show that BT = - B If (I + B³) and (I – B³) are both invertible and (I − B³)−¹(I + B³) = (I + B³) (IB³)-1. Show that C is orthogonal. (Hint: reduce CT to C-¹ by using (a))
Transcribed Image Text:Let A = [Cine (a) (b) sin Ꮎ nº], B = (1 − A)(I + A)−¹ and C = (I − B³) (I + B³)−1 -1 COS Assume (I + A)-¹ = (1 + A−¹)/ det(I + A). Show that BT = - B If (I + B³) and (I – B³) are both invertible and (I − B³)−¹(I + B³) = (I + B³) (IB³)-1. Show that C is orthogonal. (Hint: reduce CT to C-¹ by using (a))
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