Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Algebra of Linear Transformations
Consider ℝ and ℚ[x] as vector spaces over ℚ. Which of the following statements are true?
1
There exists an injective Q-linear transformation T : ℝ → ℚ[x]
2
There exists an injective ℚ-linear transformation T : ℚ[x] → ℝ
3
The ℚ-vector spaces ℚ[x] and ℝ are isomorphic
4
There do not exist non-zero ℚ-linear transformations T : ℝ → ℚ[x]