Re: subspace of a vector space

But how can i show that it is closed under addition when, the
distributive laws cannot be applied as we need to establish that it is
indeed a subspace of a vector space?




Arturo Magidin wrote:
In article <1157224675.040058.262340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
jennifer <scrilla_12_1999@xxxxxxxxx> wrote:
Is this a subset of F^3 ?

{(x_1,x_2,x_3) in F^3 : X_1+2X_2+3X_3 = 0}

Does the O vector exist?

First, I will answer the questions you actually asked:

Yes, that is a subSET of F^3, by construction.

Yes, the 0 vector does exist.

Second, I will point out that what you asked is not what you really
meant to ask.

Third, I will make a wild and amazing guess at what you actually meant
to ask:

Is the given set a subSPACE of F^3?
Does the given set CONTAIN the zero vector?

The answer to both questions is "yes".


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

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