Answer this linear algebra question with all the steps. Let U be a subspace of Rn, and x = Rn. Prove that x Є U if and only if projʊ (x) = x.

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Let U be a subspace of Rn, and x = Rn. Prove that x Є U if and only if projʊ (x) = x.

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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Question

Answer this linear algebra question with all the steps.

Let U be a subspace of Rn, and x = Rn. Prove that x Є U if and only if projʊ (x) = x.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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