(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.)
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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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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