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# Question on spanning sets Watch

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1. Let {v1, v2,..vn} be a spanning set for V, and let v be any other vector in V. Show that {v1, v2, vn, v} are linearly dependent.

Now I know that a spanning set is all the linear combinations so cv1 + cv2 + .. cvn.
This means that are linearly dependent as they rely on each other?

So adding another vector means that they are still linearly dependent?

I've probably got this completely wrong. Any help?!
2. Well, v lies in the span of the other vectors, so that means there is a non-trivial linear combination of v and the other vectors which sums to 0. This shows that the union is linearly dependent.

Note that your original set of vectors may be linearly independent. Check that you understand the definitions.

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Updated: December 10, 2010
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