(1 pt) Are the following statements true or false? ? 1. If Ax = Xx for...

 

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(1 pt) Are the following statements true or false? ? 1. If Ax = Xx for some vector x, then A is an eigenvalue of A. ? 2. To find the eigenvalues of A, reduce A to echelon form. ? 3. A matrix A is singular if and only if 0 is an eigenvalue of A. ? 4. A number c is an eigenvalue of A if and only if the equation (A - I)x = 0 has a nontrivial solution x. ? 5. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. (1 pt) Are the following statements true or false? ? 1. If Ax = Xx for some vector x, then A is an eigenvalue of A. ? 2. To find the eigenvalues of A, reduce A to echelon form. ? 3. A matrix A is singular if and only if 0 is an eigenvalue of A. ? 4. A number c is an eigenvalue of A if and only if the equation (A - I)x = 0 has a nontrivial solution x. ? 5. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.