(1) Show that I + Y X is also invertible. (2) Show that Y (I + XY )−1 = (I + Y X)−1Y .
(1) Show that I + Y X is also invertible. (2) Show that Y (I + XY )−1 = (I + Y X)−1Y .
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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Given a m ×n matrix X and a n ×m matrix Y , suppose I +XY is invertible.
(1) Show that I + Y X is also invertible.
(2) Show that Y (I + XY )−1 = (I + Y X)−1Y .
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