Hi all,
Here's a question I'm struggling with:
Show that the set of all elements of R^2 of the form (a, -a), where a is any real number, is a subspace of R^2. Give a geometric interpretation of the subspace. Any suggestions?
Thanks,
Jim
Hi all,
Here's a question I'm struggling with:
Show that the set of all elements of R^2 of the form (a, -a), where a is any real number, is a subspace of R^2. Give a geometric interpretation of the subspace. Any suggestions?
Thanks,
Jim
Note: for all vectors the first and second component must be addative inverses.
let $\displaystyle v_1=(x,-x)$ and
$\displaystyle v_2=(y,-y)$ be any vectors in the subspace
Then
$\displaystyle v_1+v_2=(x,-x)+(y,-y)=(x+y,-x-y)=(x+y,-(x+y))$
Since the first and 2nd components are addative inverses the same is closed under vector addition.
I hope this helps.