- #1

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## Homework Statement

This is probably a very dumb question, but I just can't wrap my head around what I'm supposed to be doing.

The question is:

"Determine whether the set is a subspace of R

^{3}:

All vectors of the form (a,b,c) where a = 2b + 3c"

## Homework Equations

u + v is an element of R

^{3}

ku is an element of R

^{3}

## The Attempt at a Solution

My question is.. is R

^{3}just the set of all vectors with 3 terms..(a,b,c), (d,e,f)...etc? OR does it mean that the vector I get after multiplying by the scalar has to be of the same form as u, such that a = 2b + 3c

I think I'm phrasing this wrong so I will give an example.

Let's say I am checking vector addition.

So u = (2b + 3c, b, c) and v = (2e + 3f, e, f)

When I add them I get (2b+3c+2e+2f, b+e, c+f)

Is that in R

^{3}since it has 3 terms which in fact would make it a vector space? Or do I need to check if the first term (2b + 3c + 2e + 2f) = 2(b+e) + 3(c+f) ?