7. Let V be a vector space and l: V → R be a linear map. If z E V is not in the nullspace of l, show that every r E V can be decomposed uniquely as r = v+ cz, where v E V is in the nullspace of l and cER is a scalar.
7. Let V be a vector space and l: V → R be a linear map. If z E V is not in the nullspace of l, show that every r E V can be decomposed uniquely as r = v+ cz, where v E V is in the nullspace of l and cER is a scalar.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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