1. Let matrix A, B, A + B, Al + B' are nxn non-singular matrices (a non-singular matrix means it has an inverse), prove: (Al + B-)-1 = B - B (A + B)-' B
1. Let matrix A, B, A + B, Al + B' are nxn non-singular matrices (a non-singular matrix means it has an inverse), prove: (Al + B-)-1 = B - B (A + B)-' B
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.3: Properties Of Determinants
Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
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Transcribed Image Text:1. Let matrix A, B, A + B, A' +B' are nxn non-singular matrices (a non-singular
matrix means it has an inverse), prove:
(А1 + в)1 %3 вВ - В (А + B)1 В
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