Chapter 7.1, Problem 68E

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) Geometrically, if $\lambda$ is an eigenvalue of a matrix A and x is an eigenvector of A corresponding to $\lambda$, then multiplying x by A produce a vector $\lambda \text{x}$ parallel to $\text{x}$.

(b) If A is $n\times n$ matrix with an eigenvalue $\lambda$, then the set of all eigenvectors of $\lambda$ is a subspace of $R^n$.