4. Let X = {(t,co): te R} U {[t, oo): te R}. Consider the binary relation C on X, that is, a Cy if and only if z is a subset of y. (a) Show that is complete and transitive. (b) If u: X → R is a utility representation C, show that u((t,0)) > u([t, ∞)) for every tER and u([t, ∞)) > u((s, ∞)) for every s, tER with s

Q: Let T : R" → R™ be a linear transformation, and let {V₁, V2, 73} be a linearly dependent set in R”.…

A: T: ℝn→ℝm is a Linear transformation  v1→, v2→, v3→ be a linearly dependent set in ℝn

Q: 4. Suppose that T : R* → R² is a linear map defined by T (x1, x2, x3, x4) = (2x1 x2 + x3, -2x1 – x2…

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Q: 3: Show that if T : R³ →R is a non-zero linear map, then it must be given by T = ax + by + cz for…

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Q: 8. Let T: M₂2 → R² be defined as 7 ([a b]) = (a − b, cd). Determine whether or not 7 is a linear…

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Q: 2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy…

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Q: T(x1, x2, x3, X4) = (x2 + x3, 0, x2 + x3, x3 + x4) %3D a. Show that whether the following is linear…

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Q: Let T : M2×2 → M2×2 be a mapping defined by T (A) = AT − A for A ∈ M2×2. (a) Show that T is a linear…

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Q: Which one(s) of the requirements of isomorphism does H : R" → Rª fail to satisfy? H((S1, S2, S3, S4,…

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Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

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Q: = A: a) Let T be a linear functional from R³ to R. Show that there are 3 real a,b,c such that T((x,…

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Q: 3. Suppose V is finite-dimensional and S, T are linear operators on V. Prove that ST is invertible…

A: Proof are in given below Explanation:Step 1:

Q: ¹([])=[+] 5. Let T: R2 R2 be a linear transformation defined by T a) Find a basis for Null(T) b)…

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Q: . Let B(X, Y) denote the space of all bounded linear operators between the normed spaces X and Y.…

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Q: 8. Suppose T: V V is a linear operator on an inner product space V. If T has an adjoint (hence, a…

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Q: Let →a=⟨−4,1,−2⟩a→=⟨-4,1,-2⟩ and →b=⟨−2,−3,4⟩b→=⟨-2,-3,4⟩. Find the projection of →bb→ onto →aa→.…

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Q: 3. Let T: M₂2 → R² be defined as T ( [])=(a - b, cd). Determine whether or not I' is a linear…

A: I have given the answer in the next step. Hope you understand that

Q: Can you help me explain why T is onto if Rank(T)=2 ?

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