Mathematics · Linear Algebra
Let A = matrix with rows [0,1,0,0], [1,0,0,0], [0,0,1,1], [0,0,1,1] and consider the symmetric bilinear form on &DoubleStruckCapitalR; 4 given by ⟨v, w⟩ = v t Aw, for v, w ∈ &DoubleStruckCapitalR; 4 . Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Every eigenvalue of A 2 is positive
- 2⟨u, v⟩ ≠ ⟨u, w⟩ for all non-zero vectors u, v, w with v ≠ w
- 3There exist non-zero vectors v, w such that ⟨v, w⟩ = 0✓
- 4A is invertible
Correct answer
There exist non-zero vectors v, w such that ⟨v, w⟩ = 0
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