Let V be a a) Show that im(S+T) is a subspace of im(S) + im(T). b) Show that rank(S+T) ≤ rank(S) + rank(T). c) Show that null(S+T) ≥ null(S) + null(T) - dim(V). finite-dimensional vector space and let S, T = L(V).
Let V be a a) Show that im(S+T) is a subspace of im(S) + im(T). b) Show that rank(S+T) ≤ rank(S) + rank(T). c) Show that null(S+T) ≥ null(S) + null(T) - dim(V). finite-dimensional vector space and let S, T = L(V).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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