Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Algebra of Linear Transformations
Let : T : ℝ4 → ℝ4 be a linear map with four distinct eigenvalues and satisfying T4 - 15T2 + 10T + 24I = 0. Which of the following statements are necessarily true?
1
There exists a non-zero vector v1 ∈ ℝ4 such that Tv1 = 2v1
2
There exists a non-zero vector v2 ∈ ℝ4 such that Tv2 = v2
3
For every non-zero vector v ∈ ℝ4 the set {2v, 3Tv} is linearly independent
4
T is a one-one function