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From: Mc Lauren Series on 3 Sep 2009 15:03
In a set of vectors, there can be a maximum of two 2-D vectors which
are linearly independent. Any set of three or more 2-D vectors are
linearly dependent.

Similalry, there can be a maximum of three 3-D vectors which are
linearly independent. Can this be generalized for N-D vectors that
there can be a maximum of N N-D vectors which are linearly
independent?
From: Robert Israel on 3 Sep 2009 15:06
Mc Lauren Series <mclaurenseries(a)gmail.com> writes:

> In a set of vectors, there can be a maximum of two 2-D vectors which
> are linearly independent. Any set of three or more 2-D vectors are
> linearly dependent.
>
> Similalry, there can be a maximum of three 3-D vectors which are
> linearly independent. Can this be generalized for N-D vectors that
> there can be a maximum of N N-D vectors which are linearly
> independent?

Look up the definition of "dimension".
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
From: Mc Lauren Series on 3 Sep 2009 15:15
On Sep 4, 12:06 am, Robert Israel
<isr...(a)math.MyUniversitysInitials.ca> wrote:
> Mc Lauren Series <mclaurenser...(a)gmail.com> writes:
>
> > In a set of vectors, there can be a maximum of two 2-D vectors which
> > are linearly independent. Any set of three or more 2-D vectors are
> > linearly dependent.
>
> > Similalry, there can be a maximum of three 3-D vectors which are
> > linearly independent. Can this be generalized for N-D vectors that
> > there can be a maximum of N N-D vectors which are linearly
> > independent?
>
> Look up the definition of "dimension".
> --
> Robert Israel              isr...(a)math.MyUniversitysInitials.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia            Vancouver, BC, Canada

Here, I am using it in the sense of components. By 2-D vectors, I mean
vectors having two components. Sorry for the confusion. What is the
answer to my question?
From: Tonico on 3 Sep 2009 15:26
On Sep 3, 10:15 pm, Mc Lauren Series <mclaurenser...(a)gmail.com> wrote:
> On Sep 4, 12:06 am, Robert Israel
>
>
>
>
>
> <isr...(a)math.MyUniversitysInitials.ca> wrote:
> > Mc Lauren Series <mclaurenser...(a)gmail.com> writes:
>
> > > In a set of vectors, there can be a maximum of two 2-D vectors which
> > > are linearly independent. Any set of three or more 2-D vectors are
> > > linearly dependent.
>
> > > Similalry, there can be a maximum of three 3-D vectors which are
> > > linearly independent. Can this be generalized for N-D vectors that
> > > there can be a maximum of N N-D vectors which are linearly
> > > independent?
>
> > Look up the definition of "dimension".
> > --
> > Robert Israel              isr...(a)math.MyUniversitysInitials.ca
> > Department of Mathematics        http://www.math.ubc.ca/~israel
> > University of British Columbia            Vancouver, BC, Canada
>
> Here, I am using it in the sense of components. By 2-D vectors, I mean
> vectors having two components. Sorry for the confusion. What is the
> answer to my question?-


The answer is yes, as long as you're talking of vectors with
components from a field, like the reals of complex.
The appropiate context though is what Robert I. already told you: look
up "dimension of vector space", in linear algebra books (or in google,
of course).

Tonio
From: Robert Israel on 3 Sep 2009 19:07
Mc Lauren Series <mclaurenseries(a)gmail.com> writes:

> On Sep 4, 12:06=A0am, Robert Israel
> <isr...(a)math.MyUniversitysInitials.ca> wrote:
> > Mc Lauren Series <mclaurenser...(a)gmail.com> writes:
> >
> > > In a set of vectors, there can be a maximum of two 2-D vectors which
> > > are linearly independent. Any set of three or more 2-D vectors are
> > > linearly dependent.
> >
> > > Similalry, there can be a maximum of three 3-D vectors which are
> > > linearly independent. Can this be generalized for N-D vectors that
> > > there can be a maximum of N N-D vectors which are linearly
> > > independent?
> >
> > Look up the definition of "dimension".
> > --
> > Robert Israel =A0 =A0 =A0 =A0 =A0 =A0
> > =A0isr...(a)math.MyUniversitysInitial=
> s.ca
> > Department of Mathematics =A0 =A0 =A0 =A0http://www.math.ubc.ca/~israel
> > University of British Columbia =A0 =A0 =A0 =A0 =A0 =A0Vancouver, BC,
> > Cana=
> da
>
> Here, I am using it in the sense of components. By 2-D vectors, I mean
> vectors having two components. Sorry for the confusion. What is the
> answer to my question?

I mean dimension in the sense of vector spaces. Once you understand
that, and see how to find the dimension of R^N, you will have the answer
to your question.
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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