Let A and B be square matrices of order n satisfying Ax = Bx for all x in Rn. (a) Find the rank and nullity of A − B. (b) Show that A and B must be identical.
Let A and B be square matrices of order n satisfying Ax = Bx for all x in Rn. (a) Find the rank and nullity of A − B. (b) Show that A and B must be identical.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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Let A and B be square matrices of order n satisfying Ax = Bx for all x in Rn.
(a) Find the rank and nullity of A − B.
(b) Show that A and B must be identical.
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