Let H be a Hilbert space. For any subset A of H, define A+. If A ≤ B ≤H, then show that: i) B CA ii) ACA¹ State conditions on A so that A¹¹ = A. 11

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Q: show that A is nondefective and use Theorem 7.4.3 to find eAt.

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Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: Let H be a Hilbert space and let S,T∈B(H). Suppose that (Sh|k) = (Th|k) for all h,k ∈H. Show that…

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Q: Let T be a self-adjoint operator on a Hilbert space H. Show that its norm is given by ||T|| = sup…

A: Given that T is a self-adjoint operator on a Hilbert space H. To prove: T=supx=1Tx,x.

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Q: Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.

A: Proof. Let x ∈ R be idempotent,

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Q: 1) Define the well-ordering property 2) For any integer a, show that gcd (5a+2, 7a+3) =1.

A: Find the attachment

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A: answer is in next step .please give a like!!

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Q: RX R:p + q = (e) {(p, q) = R X

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A: The given question can be solved as shown in step2.

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