Question

Determine whether the given statements are true/false. Justify your answer

a) If A is a square matrix and Ax = λx for some nonzero scalar λ, then x is an

eigenvector of A.

b) If λ is an eigenvalue of a matrix A, then the linear system (λI − A)x = 0 has only the

trivial solution.

c) If the characteristic polynomial of a matrix A is p(λ) = λ

2 + 1, then A is invertible.

d) If λ is an eigenvalue of a matrix A, then the eigenspace of A corresponding to λ is

the set of eigenvectors of A corresponding to λ.

e) The eigenvalues of a matrix A are the same as the eigenvalues of the reduced row

echelon form of A.




I need clarity answers and clear justification
please let me know​

Answer 1

Answer:

I think c) is the right option

Answer 2

Answer:

$\sf\blue{all \: statements \: are \: correct}$