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an indexed 4. Let L: R5 → R4 be a linear transformation, and let S = {v1, U2, U3} be subset of R5. Suppose that {L(v₁), L(v₂), L(v3)} is linearly independent. Show that S = {1, U2, U3} is linearly independent.

an indexed 4. Let L: R5 → R4 be a linear transformation, and let S = {v1, U2, U3} be subset of R5. Suppose that {L(v₁), L(v₂), L(v3)} is linearly independent. Show that S = {1, U2, U3} is linearly independent.

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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### Linear Independence in Linear Transformations #### Problem Statement Let \( L: \mathbb{R}^5 \rightarrow \mathbb{R}^3 \) be a linear transformation, and let \( S = \{v_1, v_2, v_3\} \) be an indexed subset of \( \mathbb{R}^5 \). Suppose that \( \{L(v_1), L(v_2), L(v_3)\} \) is linearly independent. Show that \( S = \{v_1, v_2, v_3\} \) is linearly independent.
Transcribed Image Text:### Linear Independence in Linear Transformations #### Problem Statement Let \( L: \mathbb{R}^5 \rightarrow \mathbb{R}^3 \) be a linear transformation, and let \( S = \{v_1, v_2, v_3\} \) be an indexed subset of \( \mathbb{R}^5 \). Suppose that \( \{L(v_1), L(v_2), L(v_3)\} \) is linearly independent. Show that \( S = \{v_1, v_2, v_3\} \) is linearly independent.
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