For a variable x, consider the &doubleunderbar;&qu;ℝ&qu;-vector space V = {ax3 + bx2 + cx + d | a, b, c, d ∈ ℚ}. Further let A = {f : V → ℚ | f is a ℚ-linear transformation} and B = {f ∈ A | f(1) = 0}. Which of the following statements is true?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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dim B = 3

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Answer 1

If f ∈ A, then the image of f is a one-dimensional ℚ-vector space.

Answer 2

If f ∈ B, then dim(ker f) = 3.

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