Exercise 2. Suppose V and W are finite-dimensional, T E L(V, W), and there exists PE W' such that null T' = Span(4). Prove that range T = null p. %3D %3D
Exercise 2. Suppose V and W are finite-dimensional, T E L(V, W), and there exists PE W' such that null T' = Span(4). Prove that range T = null p. %3D %3D
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:Exercise 2. Suppose V and W are finite-dimensional, T E L(V,W), and there exists
PE W' such that null T' = Span(4). Prove that range T = null p.
Expert Solution

Step 1
Given and are finite dimensional , and there exists such that
We have to prove that
In order to prove this we have to prove that if then
Let
then
Since,
then there exist such that
Now,
Thus
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