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 Post subject: Dimension and basis of a vector spacePosted: Fri, 4 Nov 2011 03:57:38 UTC
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Joined: Fri, 30 Oct 2009 16:33:10 UTC
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The question is: Find the dimension of the vector space V and give a basis for V. V={p(x) in P2:p(0)=0}

Well since this is P2, I know that the exponent of the polynomial must not exceed 2. So I am looking at polynomials of the form but because of the initial condition I know c=0. So what would the dimension be - ?
Also I know that the conditions for a basis are 1. that the vectors span S and 2. it is linearly independent. I am familiar with doing this for vectors, but I have never had to find a basis for a polynomial. What do I need to do to?

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 Post subject: Re: Dimension and basis of a vector spacePosted: Fri, 4 Nov 2011 05:52:27 UTC
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goteamusa wrote:
The question is: Find the dimension of the vector space V and give a basis for V. V={p(x) in P2:p(0)=0}

Well since this is P2, I know that the exponent of the polynomial must not exceed 2. So I am looking at polynomials of the form but because of the initial condition I know c=0. So what would the dimension be - ?
Also I know that the conditions for a basis are 1. that the vectors span S and 2. it is linearly independent. I am familiar with doing this for vectors, but I have never had to find a basis for a polynomial. What do I need to do to?

Not much differences --- individual polynomials are your vectors, and the space of polynomials of degree at most 2 is your vector space.

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 Post subject: Re: Dimension and basis of a vector spacePosted: Fri, 4 Nov 2011 06:05:01 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
goteamusa wrote:
The question is: Find the dimension of the vector space V and give a basis for V. V={p(x) in P2:p(0)=0}

Well since this is P2, I know that the exponent of the polynomial must not exceed 2. So I am looking at polynomials of the form but because of the initial condition I know c=0. So what would the dimension be - ?
Also I know that the conditions for a basis are 1. that the vectors span S and 2. it is linearly independent. I am familiar with doing this for vectors, but I have never had to find a basis for a polynomial. What do I need to do to?

Eh? Use the coordinate mapping to look at , then this is the space of vectors which look like so. . .

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