Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Let A be an n × n matrix with complex entries. If n ≥ 4, which one of the following statements is true?
1
A does not have any non-zero invariant subspace in ℂn.
2
A has an invariant subspace in ℂn of dimension n - 3.
3
All eigenvalues of A are real numbers.
4
A2 does not have any invariant subspace in ℂn of dimension n - 1.