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## Homework Statement

Let {x1,x2,...,x

_{k}} be a spanning set for a vector space V.

a) if we add another vector, x

_{k+1}to the set, will we still have a spanning set ? Explain

## Homework Equations

## The Attempt at a Solution

I think 'yes', but I am not sure if my explanation is correct.

It doesn't matter if they are independent or dependent, because we know that the first k vectors are independent and that's what we need to create a spanning set for V.

If the kth+1 vector is independent, the set is going to span a bigger vector space, a vector space that includes V. So, it's going to be a spanning set for V regardless of x

_{k+1}

Is my reasoning correct ?

Thanks.