Problem 2. Let V = span{e3, e-3z}, and let the linear transformation D : V → V be differentiation with respect to x. One basis of V is C = {cosh(3x), sinh(3x)}, where e3z + e-3z e3z – e-3z cosh(3x) sinh(3r) %3D 2 The matrix of D with respect to C is A = 3 (a) Find the eigenvalues X1, X2 of A, and corresponding eigenvectors u (b) Explain what happens when we apply D to the elements u1 cosh(3x)+u2sinh(3x) and vị cosh(3x) + v½ sinh(3x) of V. 2.
Problem 2. Let V = span{e3, e-3z}, and let the linear transformation D : V → V be differentiation with respect to x. One basis of V is C = {cosh(3x), sinh(3x)}, where e3z + e-3z e3z – e-3z cosh(3x) sinh(3r) %3D 2 The matrix of D with respect to C is A = 3 (a) Find the eigenvalues X1, X2 of A, and corresponding eigenvectors u (b) Explain what happens when we apply D to the elements u1 cosh(3x)+u2sinh(3x) and vị cosh(3x) + v½ sinh(3x) of V. 2.
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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Linear Methods

Transcribed Image Text:Problem 2. Let V = span{e3z, e-3¤}, and let the linear transformation D : V → V
be differentiation with respect to x. One basis of V is
с 3 {сosh(Зx), sinh(3x)},
where
e3r + e-3z
e3r -
-3x
cosh(3x)
sinh(3x)
2
The matrix of D with respect to C is
A =
3 0
(a) Find the eigenvalues A1, A2 of A, and corresponding eigenvectors
u
V =
u2
(b) Explain what happens when we apply D to the elements u1 cosh(3x)+u2 sinh(3x)
and vị cosh(3x) + v2 sinh(3x) of V.
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