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#### karush

##### Well-known member

- Jan 31, 2012

- 2,660

$\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.