Practice question · True or false
Adding a vector to a list always enlarges its span.
Hints
- What if the new vector is already reachable?
- A multiple of an existing vector adds nothing.
Show the answer
False
Why
False. If the new vector already lies in the span — a multiple of one you have, or any combination of them — the span is unchanged. The span grows only when the vector is independent of the existing ones, which is exactly what makes independence the right notion for measuring dimension.
Practise Span and Linear Combinations
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More questions on Span and Linear Combinations
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