Chapter 7.1, Problem 67E

True or False? In Exercises 67 and 68, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) The scalar $\lambda$ is an eigenvalue of an $n\times n$ matrix A when there exists a vector x such that $Ax=\lambda x$.

(b) To find the eigenvalue(s) of an $n\times n$ matrix A. you can solve the characteristic equation $\det \left(\lambda I-A\right)=0$.