Answer with explanation please A is an n times n matrix Chec

Answer with explanation please

A is an n times n matrix. Check the true statement below: An eigenspace of A is just a null space of a certain matrix. If nu1 and nu2 are linearly independent eigenvector, then they correspond to distinct eigenvalue. If Ax = lambda x for some vector x, then x is an eigenvector of A. A steady-state vector for a stochastic matrix is actually an eigenvector. The eigenvalues of a matrix are on its main diagonal.

Solution

A. True

Let, t be an eigenvalue and v corresponding eigenvector

Hence, (A-tI)v=0

B. False

Consider the identity amtrix, It has only 1 eigenvalue but n distinct eigenvectors.

C. True

And lambda is the eigenvalue

D. True

Av=0 , where v is steady state vector

v is eigenvector with eigenvalue 0

E. False