Equality of Span Sets

• To prove equality of sets we need to prove that both sets are subsets ($\subseteq$) of each other.

• So if $A\subseteq B$ and $B\subseteq A$ then $A=B$.

• To prove Span A $\subseteq$ Span B.

• We need to prove that an element in Span A can be expressed as a linear combination of elements in Span B.

• And vice-versa.

• If proving Span A $\subseteq R^n$.

• We know that $R^n$ is closed under linear combination so it’s just a one line proof.