Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Algebra of Linear Transformations
Let T : ℝ5 → ℝ5 be a R-linear transformation. Suppose that (1, -1, 2, 4, 0), (4, 6, 1, 6, 0) and (5, 5, 3, 9, 0) span the null space of T. Which of the following statements are true?
1
The rank of T is equal to 2.
2
Suppose that for every vector v ∈ ℝ5, there exists n such that Tnv = 0. Then T2 must be zero.
3
Suppose that for every vector v ∈ ℝ5, there exists n such that Tnv = 0. Then T3 must be zero.
4
(-2, -8, 3, 2, 0) is contained in the null space of T.