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The set: V = {Ae²* sin(3x) + Be² cos (3x) : A, B = R} consists of all the solutions of the differential equation: d'y dx² dy 4- + 13y = 0 dx and forms a vector space over R with the usual addition and scalar multiplication operations.

The set: V = {Ae²* sin(3x) + Be² cos (3x) : A, B = R} consists of all the solutions of the differential equation: d'y dx² dy 4- + 13y = 0 dx and forms a vector space over R with the usual addition and scalar multiplication operations.

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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The set: V = {Ae²* sin(3x) + Be² cos (3x): A, B = R} consists of all the solutions of the differential equation: d'y dx² dy 4 + 13y = 0 dx and forms a vector space over R with the usual addition and scalar multiplication operations.
Transcribed Image Text:The set: V = {Ae²* sin(3x) + Be² cos (3x): A, B = R} consists of all the solutions of the differential equation: d'y dx² dy 4 + 13y = 0 dx and forms a vector space over R with the usual addition and scalar multiplication operations.
Let W be a vector space. Let h: W → W be a linear map. Show that h is injective (that is, h(w₁) = h(w₂) only when w₁ = W₂) if and only if ker(h) = {0}.
Transcribed Image Text:Let W be a vector space. Let h: W → W be a linear map. Show that h is injective (that is, h(w₁) = h(w₂) only when w₁ = W₂) if and only if ker(h) = {0}.
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