Mathematics · Inner Product Spaces
Let n be a positive integer and F be a non-empty proper subset of {1, 2, ..., n}. Define ⟨x, y⟩ F = ∑ k∈F x k y k , where x = (x 1 , ..., x n ), y = (y 1 , ..., y n ) ∈ ℝ n . Let T = {x ∈ ℝ n : ⟨x, x⟩ F = 0}. For y ∈ ℝ n , y ≠ 0, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1sup x∈T ⟨x + y, x + y⟩ F < ⟨y, y⟩ F
- 2inf x∈T ⟨x + y, x + y⟩ F < ⟨y, y⟩ F
- 3sup x∈T ⟨x + y, x + y⟩ F = ⟨y, y⟩ F
- 4inf x∈T ⟨x + y, x + y⟩ F = ⟨y, y⟩ F✓
Correct answer
inf x∈T ⟨x + y, x + y⟩ F = ⟨y, y⟩ F
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