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Show that W is a subspace of V over R where W = {f(r)|f(3) = 0}.

Show that W is a subspace of V over R where W = {f(r)|f(3) = 0}.

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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(7.) Show that W is a subspace of V over R where W = {f(x)|f(3) = 0}. (8.) Show that W is not a subspace of V where W = {f(x)|ƒ(7) = 2+ f(1)}.
Transcribed Image Text:(7.) Show that W is a subspace of V over R where W = {f(x)|f(3) = 0}. (8.) Show that W is not a subspace of V where W = {f(x)|ƒ(7) = 2+ f(1)}.
Show that V = R² is not a vector space over R with respect to the following operations: (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (ka, b).
Transcribed Image Text:Show that V = R² is not a vector space over R with respect to the following operations: (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (ka, b).
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