Exercise I.A.6

Question

Suppose $A$ and $B$ are subsets of the vector space $V$; show that if $A\subseteq B$, then $\mathrm{span}(A) \subseteq \mathrm{span}(B)$.

Toğrul Topal · Accepted Answer

All subspaces $B_\alpha$ that contain $B$ automatically contain $A$ too. Thus the set of all subspaces of $V$ containing $B$ is a subset of the set of all subspaces of $V$ containing $A$. Since we take the intersection over a larger number of sets $\{B_\beta\}_{\beta \in I_1} \subseteq \{A_\alpha\}_{\alpha \in I_2}$, it must be that $\bigcup_{\beta \in I_1} B_\beta \supset \bigcup_{\alpha \in I_2} A_\alpha$

Exercise I.A.6

Answers

Comments

Exercise I.A.6

Answers

Comments

Add answer