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...

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<br>space W. Prove that the range of T is a subspace of W. [Hint: Vectors in the range<br>of T have the form T(v) for some v in V.]<br>[p(0)]<br>[P(1)|<br>For example if p(t) = 3 + 4t + 5t² then T(p) = :<br>4. Define T : P2 → R² by T(p)<br>(a) Show that T is a linear transformation.<br>(b) Find a polynomial in the kernel of T.<br>(c) What is the range of T?<br>

Extracted 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?

Jun 05, 2022

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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...

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