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 vectorspace W. Prove that the range of T is a subspace of W. [Hint: Vectors in the rangeof 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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Answered: Let T : V → W be a linear…

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 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.]