A is an n x n matrix. Check the true statements below: DA. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. B. A number c is an...

Extracted text: A is an n x n matrix. Check the true statements below: DA. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. B. A number c is an eigenvalue of A if and only if the equation (A – cI)æ = 0 has a nontrivial solution x. C. To find the eigenvalues of A, reduce A to echelon form. D. If Ax = Ax for some vector æ, then A is an eigenvalue of A. E. A matrix A is not invertible if and only if O is an eigenvalue of A.