Mathematics · Linear Algebra
Consider ℝ and ℚ[x] as vector spaces over ℚ. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There do not exist non-zero ℚ-linear transformations T : ℝ → ℚ[x]
- 2The ℚ-vector spaces ℚ[x] and ℝ are isomorphic
- 3There exists an injective ℚ-linear transformation T : ℚ[x] → ℝ✓
- 4There exists an injective ℚ-linear transformation T : ℝ → ℚ[x]
Correct answer
There exists an injective ℚ-linear transformation T : ℚ[x] → ℝ
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