Let S = {f: (a, b] → R such that f () = f(a) + 2f (b)}. (a+b' (A) Show that there exists the additive identity of the set, and find it. (solution) (B) Determine whether the set is closed under addition or not. (solution) (C) Determine whether the set is closed under scalar multiplication or not. (solution) (D) Determine whether the set is a vector space or not. (solution)

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A: By the set inequality i have solved the problem

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A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

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Q: For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

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A: Here, in the question, there are given the bounded linear operators l1→l∞ which are given as…

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A: Given,If A²=0, prove that A cannot be invertible.

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Q: What theorem(s) from linear algebra are used to prove Existence and Uniqueness? In linear algebra,…

A: Theorem(s) used to prove Existence and Uniqueness: The Existence and Uniqueness Theorem for systems…

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Q: A: pp. A: px p. . A: pp(3)x3 + p(1)x.

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Q: is bijection. Do the same thing with Z,.

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Q: a;jA = Aô;*, Show that where A is a determinant of order three and A" are cofactors of a.

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Q: Let TA an operator from R2 to R2. W(w1, w2) = TĄ(X1, x2) W1 = -2X1 + 6x2 W2 = 3X1 + 1X2 if TA is…

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Q: 2c

A: The answer has been provided.Explanation:

Q: Give an example of a linear operator TE L(R*") which is not diagonalizable. Justify your answer.

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Q: What is the coefficient What is the coefficient of rx3x3 in (x₁ + x2 + x3 − x4 - x5)⁹? 1 13 of 2¹3…

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A: For the 2*2 matrix we can find determinants by multiplying the diagonal numbers and find the…

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Q: 3. Let A, B, T be bounded self-adjoint linear operators on a complex Hilbert space H. If T20 and…

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Q: (c) For a polynomial p = a + a₁x + a₂x² + + anx", let p denote the polynomial obtained from p by…

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Q: Use the Second Shift Theorem to determine i. F(3te-(t+5)²) F-1 e3(w+2)j ii. 3+(w-5)j

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Q: Consider the set C of complex numbers. Let (c², d) be a function where c² represents an element from…

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