# [SOLVED]10.2 Determine if the set of vectors form a vector space

#### karush

##### Well-known member
Determine if the set of vectors
$\begin{bmatrix} x\\y\\5 \end{bmatrix}\in \Bbb{R}^3$
form a vector space
ok if I follow the book example I think this is what is done
$\begin{bmatrix} x_1\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5 \end{bmatrix} =\begin{bmatrix} x_1+x_2+x_3\\y_1+y_2+y_3\\15 \end{bmatrix}$
since the third entry is 15, the set of such vectors is not closed under addition and hence is not a subspace

I assume in this case a vector space and sub space are the same.

#### Ackbach

##### Indicium Physicus
Staff member
Right: sub spaces are by definition vector spaces in their own right. Your proof looks good to me! What if the third component was zero?

#### karush

##### Well-known member
well if the 3rd conponent is zero then everying is just on the same plane
so multiplication or addition would close

well i think anyway?

#### topsquark

##### Well-known member
MHB Math Helper
Didn't you post this question somewhere else many moons ago? I could swear that I responded to this one at some point in the past.

-Dan

#### karush

##### Well-known member
I don't think so

But I took linear Algebra a year ago it might be very similar..

They combined the LA and De class
Not sure why.

I mark the hw probs I go to MHB for help with the MHB logo to avoid dbb.

But I post a lot since I'm very deaf and classroom is nil to me.