Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R, (b) Let and 0 represent the functions e2", xe2a and x?e2a, respectively. 3 For example, 4 represents 3e2a + 4xe2a + 5x²e2«. Find the matrix of differentiation as a linear transformation on V.
Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R, (b) Let and 0 represent the functions e2", xe2a and x?e2a, respectively. 3 For example, 4 represents 3e2a + 4xe2a + 5x²e2«. Find the matrix of differentiation as a linear transformation on V.
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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![Let V = span{e2", xe2ª , x²e2¤}.
(a) Show that
d
dx
+ agze?r + аҙӕ*е2) € V for any aj, az, aҙ € R,
(b)
Let 0
and
represent the functions e2a, xe2* and x²e2x.
respectively.
For example, 4 represents 3e2 + 4xe2a + 5x²e2ª.
5
Find the matrix of differentiation as a linear transformation on V.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51be4038-25b0-462c-88b7-f9d17375dd0c%2F53f481cb-64ed-4ff3-acd9-0240c0a869a4%2Fi9p7xc9_processed.png&w=3840&q=75)
Transcribed Image Text:Let V = span{e2", xe2ª , x²e2¤}.
(a) Show that
d
dx
+ agze?r + аҙӕ*е2) € V for any aj, az, aҙ € R,
(b)
Let 0
and
represent the functions e2a, xe2* and x²e2x.
respectively.
For example, 4 represents 3e2 + 4xe2a + 5x²e2ª.
5
Find the matrix of differentiation as a linear transformation on V.
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