Answer
(a) True.
(b) False.
Work Step by Step
(a) True.
This by Theorem 4.10.
(b) False.
This is not true. For example, $W=\{(1,1,1), (2,2,2)\}$ is a subset of
$R^3$ which is is a vector space of dimension $3$, however, $W$ is a linearly dependent set of vectors.
