Practice question · Multiple choice
The span of a set is always a subspace, whatever vectors you start from. Why is that automatic?
Hints
- Add two linear combinations of the same vectors and look at the result.
- Check the three subspace conditions one at a time.
Show the answer
B. Because a span is by construction closed under addition and scaling
Why
The three conditions fall out of the definition. This is why "span" is the standard way to BUILD a subspace: you cannot fail to get one.
Practise Span and Linear Combinations
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