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Let V be a vector space and let T: V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W Range(T – I), where I : V → V is the identity. II (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T + 21).

Let V be a vector space and let T: V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W Range(T – I), where I : V → V is the identity. II (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T + 21).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let V be a vector space and let T : V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W = Range(T – I), where I :V → V is the identity. - (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T+ 21).
Transcribed Image Text:Let V be a vector space and let T : V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W = Range(T – I), where I :V → V is the identity. - (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T+ 21).
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