Prove the part of the theorem which lets w be any solution of Ax=b, and defines v₁=w-p. Show that Vh is a solution of Ax=0. This shows that every solution of Ax=b has the form w=p+Vh, with p a 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. Avh=A( What theorem should be used next? A. Ax=x₁a₁ + X₂ª₂ + ... +Xnan OB. u+v=v+u C. A(cu) = c(Au) D. A(u + v) = Au + Av Use that theorem to change the right side of the equation found above. Av₁ = Simplify the right side of the equation that was just found. Av₁ = So Av₁ = Thus, vis a solution of Ax = 0.
Prove the part of the theorem which lets w be any solution of Ax=b, and defines v₁=w-p. Show that Vh is a solution of Ax=0. This shows that every solution of Ax=b has the form w=p+Vh, with p a 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. Avh=A( What theorem should be used next? A. Ax=x₁a₁ + X₂ª₂ + ... +Xnan OB. u+v=v+u C. A(cu) = c(Au) D. A(u + v) = Au + Av Use that theorem to change the right side of the equation found above. Av₁ = Simplify the right side of the equation that was just found. Av₁ = So Av₁ = Thus, vis a solution of Ax = 0.
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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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 p a particular solution of Ax = b and v₁
a solution of Ax = 0.
Let w and p be solutions of Ax = b. Substitute for vn from the equation w=p+Vh
Av=A(
What theorem should be used next?
+Xnªn
A. Ax=x₁ª₁ + X₂³₂ +
B. u+v=v+u
C. A(cu) = c(Au)
D. A(u + v) = Au + Av
Use that theorem to change the right side of the equation found above.
Av₁ =
Simplify the right side of the equation that was just found.
Av₁ =
So Av₁ =
Thus, vis a solution of Ax = 0.
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