Let T : V → W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W. [Hint: Vectors in the range of T have the form T(v) for some v in V.]
Let T : V → W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W. [Hint: Vectors in the range of T have the form T(v) for some v in 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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please sove both problems im having trouble on them
![3. Let T : V → W be a linear transformation from a vector space V into a vector
space W. Prove that the range of T is a subspace of W. [Hint: Vectors in the range
of T have the form T(v) for some v in V.]
[p(0)]
[P(1)|
For example if p(t) = 3 + 4t + 5t² then T(p) = :
4. Define T : P2 → R² by T(p)
(a) Show that T is a linear transformation.
(b) Find a polynomial in the kernel of T.
(c) What is the range of T?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa51cb2c6-68d7-460b-b6c2-8a3d6ada438a%2F27986015-3128-448f-b487-b5320cec332b%2Ft308x4q_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let T : V → W be a linear transformation from a vector space V into a vector
space W. Prove that the range of T is a subspace of W. [Hint: Vectors in the range
of T have the form T(v) for some v in V.]
[p(0)]
[P(1)|
For example if p(t) = 3 + 4t + 5t² then T(p) = :
4. Define T : P2 → R² by T(p)
(a) Show that T is a linear transformation.
(b) Find a polynomial in the kernel of T.
(c) What is the range of T?
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