# I need the answer to problem 4 (exercises 1, 2, 3) Clear and step by step...

I need the answer to problem 4 (exercises 1, 2, 3)

Clear and step by step please Problem 4. Let V be a vector space and let T : V → V and U : V → V be two linear transforinations 1. Show that. TU is also a linear transformation. 2. Show that aT is a linear transformation for any scalar a. 3. Suppose that T is invertible. Show that T-1 is also a linear transformation. Problem 5. Let T : R3 → R2 be a linear transformatio! 1. State the Dimension Theorem for T. 2. Show that T is not 1-1. 3. Give an example for which T is onto. Give an example for which T is not onto. (In each case show that your example has the required property. Do not just give an example with no explanation). Problem 6, Let T : V → W be a linear map. Suppose that it is one-to-one. Suppose th be the images . . . . ,蚴is a linearly independent subset of V. Let wi 2], . . . ,we-Tuk. Show that w].. that { uh are linearly independent. ##### Add Answer of: I need the answer to problem 4 (exercises 1, 2, 3) Clear and step by step...
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• ### 1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1,... 1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...

• ### Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem... Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...

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2. Let V and W be vector spaces and T: V－>W be a linear transformation. For a given U subset of V,we denote byT(U)the subset of W deined byT(U)= {T(u)|uε U}.(a) Prove that T is one-to-one if and only if for every linearly independent subset U of V, the subsetT(U) of W is linearly independent.(b) Assume that V={v1,...,vn} is a basis for V and that T is one-to-one and onto. Prove that T(V) is a basis for W.c) Assume that...

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• ### Please answer me fully with the details. Thanks! True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linear... Please answer me fully with the details. Thanks! True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linearly independent subset of (1) Let V bea vector spacе, аnd let dim(V) V. then n < т. (2) Let V and W be vector spaces, and suppose that T : V -+ W is a linear transformation. If there are vectors i, 2, ..., Tj in V such that the vectors T(),T(T2),...,T(vj) span W, then the...

• ### 101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1... 101-2019-3-b (1).pdf-Adobe Acrobat Reader DC Eile Edit iew Window Help Home Tools 101-2019-3-b (1) Sign In x Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y, x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V -> V such that U is not an...

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