- #1

Ryker

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## Homework Statement

Determine if the following subset of R

_{n}is a subspace: all vectors <a

_{1}, a

_{2}, ... , a

_{n}>, such that a

_{1}= 1.

## Homework Equations

## The Attempt at a Solution

I'm going through the Linear Algebra: An Introductory Approach by Curtis and found this thing. I can't quite get around the fact on why this isn't a subspace. Can someone explain perhaps? How do I even start doing this? I tried setting up two different vectors, the first one <k, k

_{2}a

_{2}, ... , k

_{n}a

_{n}> and the second one <l, l

_{2}a

_{2}, ... , l

_{n}a

_{n}>, and then adding them up. But I don't even know what I'm supposed to be looking for.

edit: Or do k and l need to be 1 here? Because I guess then it's not hard seeing that multiplying such a vector by a scalar would result in a vector whose first coordinate isn't one, and that adding two, whose first coordinates are 1, amounts to the first one being 2. Hence, this would not be a subspace, because these resultant vectors would lie outside of our conditions.

Still, even if this is the case, this one is really basic, and I'm still having trouble getting my head around how to tackle more complicated cases.

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