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(2) Let V be a subspace of Rn and T : R" → Rm be a linear transformation. Show that T(V) = {T(v) : 7 € V} is a subspace of Rm and dim(V) ≥ dim(T(V)). (Hint: let {₁,...,} be a basis for V.)

(2) Let V be a subspace of Rn and T : R" → Rm be a linear transformation. Show that T(V) = {T(v) : 7 € V} is a subspace of Rm and dim(V) ≥ dim(T(V)). (Hint: let {₁,...,} be a basis for V.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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(2) Let V be a subspace of Rn and T: Rn → Rm be a linear transformation. Show that T(V) = {T(v) : 7 € V} is a subspace of Rm and dim(V) ≥ dim(T(V)). (Hint: let {vi,...,} be a basis for V.)
Transcribed Image Text:(2) Let V be a subspace of Rn and T: Rn → Rm be a linear transformation. Show that T(V) = {T(v) : 7 € V} is a subspace of Rm and dim(V) ≥ dim(T(V)). (Hint: let {vi,...,} be a basis for V.)
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