Mathematics · Linear Algebra
Let I denote the 3 × 3 identity matrix. Given any three distinct matrices A, B, C ∈ M3(&mathbb;R), which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There exists D ∈ M3(&mathbb;R) and a polynomial f ∈ &mathbb;R[X] satisfying f(A) = f(B) = f(C) = 0 and f(D) = I.
- 2There exists D ∈ M3(&mathbb;R) and a polynomial f ∈ &mathbb;R[X] satisfying f(A) = f(B) = 0, f(C) = I, and f(D) = I.
- 3There exists D ∈ M3(&mathbb;R) and a polynomial f ∈ &mathbb;R[X] satisfying f(A) = 0, f(B) = f(C) = I, and f(D) ≠ 0.✓
- 4There exists D ∈ M3(&mathbb;R) and a polynomial f ∈ &mathbb;R[X] satisfying f(A) = f(B) = 0, f(C) = I, and f(D) = 0.
Correct answer
There exists D ∈ M3(&mathbb;R) and a polynomial f ∈ &mathbb;R[X] satisfying f(A) = 0, f(B) = f(C) = I, and f(D) ≠ 0.
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