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|.
Question
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
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
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Inverse of a Matrix
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning