Practice question · Select all that apply
Which statements about span and independence are true?
Hints
- Check what happens when the zero vector joins a set.
- It can always be combined with a nonzero coefficient to give zero.
Show the answer
- A. In a basis, every vector of the space has unique coordinates
- C. Adding a dependent vector to a set leaves the span unchanged
- D. Two independent vectors in span the whole plane
Why
The zero vector is everyone’s dependent friend ( is a nonzero-coefficient combination giving zero), so it poisons independence instantly. The rest are the core theorems.
Practise Vector Spaces
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