Suppose T E L(V, W), and w1, ..., wm is a basis of range T.
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:Suppose T E L(V, W), and w1, ..., wm is a basis of range T. Prove that
there exist o1,..., Om € L(V, F) such that
Tv = 91(v)w1 +…+ &m(v)Wm
..
for every v e V.
Hint: We need to show that pi is a linear transformation.
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