Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Linear Dependence, Basis & Dimension
Let V (≠{0}) be a finite dimensional vector space over ℝ and T: V → V be a linear operator. Suppose that the kernel of T equals the image of T. Which of the following statements are necessarily true?
1
The dimension of V is even
2
The trace of T is zero
3
The minimal polynomial of T cannot have two distinct roots
4
The minimal polynomial of T is equal to its characteristic polynomial