Mathematics · Linear Algebra
Let V be the vector space of all real polynomials of degree ≤ 9. Let T: V &to; V be a linear transformation defined by T(p(x)) = p'(x) for p ∈ V. Consider the basis B = {1, x, x2, ..., x9} of V. If A is the matrix of T with respect to this basis, then:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1A has a nonzero eigenvalue
- 2There is no m ∈ N such that Am = 0
- 3det A = 0✓
- 4Trace A = 1
Correct answer
det A = 0
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