Chapter 4 - Vector Spaces - 4.6 Bases and Dimension - True-False Review - Page 308: b

False

Let $V$ is a vector space of $3\times 3$ matrices and $W$ is a set of all polynomials with degree $\leq 2$. We have dimension of $V$ is $9$ and dimension of $W$ is $3$, but we can see $W$ is not a subspace of $V$. Hence, the statement is false.