Subspace Addition Span Union

Theorem

• If $W_1=span(S_1)$ and $W_2=span(S_2)$
• Then, $W_1+W_2=span(S_1\cup S_2)$

Proof

Proving $⟹$ that $W_1+W_2\subset span(S_1\cup S_2)$ 1.

Proving $⟸$ that $span(S_1\cup S_2)\subset W_1+W_2$