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2. Let f : V → W be a homomorphism. Show that if the set S = {v1, 02, ... , Un} C V is linearly dependent, then the set S' = {f(i), f (52), ... , f(Tn)} CW is linearly dependent as well.

2. Let f : V → W be a homomorphism. Show that if the set S = {v1, 02, ... , Un} C V is linearly dependent, then the set S' = {f(i), f (52), ... , f(Tn)} CW is linearly dependent as well.

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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is a subspace of V. 2. Let f : V → W be a homomorphism. Show that if the set S = {v1, 02, . . . , Un} CV is linearly dependent, then the set S' = {f(T), f(52),. . . , f (Tn)} C W is linearly dependent as well. 3. Let h : P3 → P3 by h(a+ bx + cx² + dx³) = a + (a + b)x + (b – c)x² + (c + d)a³. Find:
Transcribed Image Text:is a subspace of V. 2. Let f : V → W be a homomorphism. Show that if the set S = {v1, 02, . . . , Un} CV is linearly dependent, then the set S' = {f(T), f(52),. . . , f (Tn)} C W is linearly dependent as well. 3. Let h : P3 → P3 by h(a+ bx + cx² + dx³) = a + (a + b)x + (b – c)x² + (c + d)a³. Find:
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