Mathematics · Linear Algebra
For a 4 × 4 positive definite real symmetric matrix A and real numbers a, b, c, d, consider the 5 × 5 matrix B given by: B = Aabcdabcd0 Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1det(B) > 0 for every nonzero (a, b, c, d) ∈ ℝ4
- 2det(B) > 0 for infinitely many (a, b, c, d) ∈ ℝ4
- 3det(B) ≤ 0 for every (a, b, c, d) ∈ ℝ4✓
- 4det(B) > 0 for at least one (a, b, c, d) ∈ ℝ4
Correct answer
det(B) ≤ 0 for every (a, b, c, d) ∈ ℝ4
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