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Prove the part of the theorem which lets w be any solution of Ax = b, and defines v₁ = w-p. Show that v₁ is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh, with pa particular solution of Ax = b and v₁ a solution of Ax = 0. Let w and p be solutions of Ax = b. Substitute for V₁ from the equation w=p+Vn AVI,-A-

Prove the part of the theorem which lets w be any solution of Ax = b, and defines v₁ = w-p. Show that v₁ is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh, with pa particular solution of Ax = b and v₁ a solution of Ax = 0. Let w and p be solutions of Ax = b. Substitute for V₁ from the equation w=p+Vn AVI,-A-

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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Prove the part of the theorem which lets w be any solution of Ax = b, and defines v₁ = w-p. Show that v₁ is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh, with pa particular solution of Ax = b and v₁ a solution of Ax = 0. Let w and p be solutions of Ax = b. Substitute for V₁ from the equation w=p+Vn AVI,-A-
Transcribed Image Text:Prove the part of the theorem which lets w be any solution of Ax = b, and defines v₁ = w-p. Show that v₁ is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh, with pa particular solution of Ax = b and v₁ a solution of Ax = 0. Let w and p be solutions of Ax = b. Substitute for V₁ from the equation w=p+Vn AVI,-A-
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