Chapter 4.1, Problem 3E

GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace.

Which of the subsets of $P_2$given in Exercises 1 through 5 are subspaces of $P_2$(see Example 16)? Find a basis for those that are subspaces.

3. $\left\{p\left(t\right):p^{\prime }\left(1\right)=p\left(2\right)\right\}\left(p^{\prime }\text{is}\text{the}\text{derivative}\right)$