Proving Spanning Sets Equivalent

Spanning sets are equivalent if:

• $span(X)\subset span(Y)$
• $span(Y)\subset span(X)$ This can be done by proving:
• $X\in span(Y)$ (shows $span(X)\subset span(Y)$)
• $Y\in span(X)$ (shows $span(Y)\subset span(X)$)

Example

Redundant Spans

You can prove equivalent spans because most spans are redundant linear combinations that can be derived from other sets.