Let X be a topological vector space. Prove that: OFor A, BC X, A+BCA+B. ) If Y is a linear subspace of X, then Y is also a lincar subspace of X. )For A CX, if A is balanced, then A is also balanced. ) For ACX, if A is bounded, then A is also bounded.

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A: To show that H is not a subspace of a vector

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A: This is a problem of Functional Analysis.

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Q: Prove that if W is a subspace of a vector space V and w1, w2, . . . , wn are in W, then a1w1 + a2w2…

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Q: 5) Determine whether the indicated subset is a subspace of the given vector space. a) (x, y, z), x,…

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Q: The empty subset of any vector space V is not a subspace of V. True False

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A: Please check step 2 for the solution.

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Q: 17. Prove that a subset W of a vector space V is a subspace of V if and only if W + Ø, and, whenever…

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Q: Let W1 and W2 be subspaces of a vector space V having ilimensions mand n, respectively, where m…

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Q: If M is a closed subspace of a Hilbert space H then H %3DМӨМ'.Prove.

A: Complete inner product space is called Hilbert space

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Q: 12) Show that subset W of a vector space V is a subspace of V if and only if span(W) = W.

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A: Solution:Hilbert space H, M⊥⊥ smallest closed subspaceWe first show that for any M⊂H, M⊥is closed.…

Q: Let V and W be subspaces of R", and dim V and dim W are strictly less than n. Assume that no…

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Q: Let W1,W2,K1,K2, . . . ,Kp,M1,M2, . . . ,Mq be subspaces of a vector space V such that W1 = K1⊕K2⊕·…

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Q: Let H be a subspace of real space R. In terms of a geometrical definition of H, which of the…

A: Given:

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