Mathematics · Linear Algebra
Let V be the vector space of all polynomials in one variable of degree at most 10 with real coefficients. Let W1 be the subspace of V consisting of polynomials of degree at most 5 and let W2 be the subspace o f V consisting of polynomials such that the sum of their coefficients is 0. Let W be the smallest su bspace of V containing both W1 and W2. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The dimension of W1 ∩ W2 is at most 5.
- 2W1 ⊆ W2.
- 3W = V.✓
- 4The dimension of W is at most 10.
Correct answer
W = V.
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