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 Post subject: how to find if this equation has a solution?Posted: Thu, 27 Oct 2011 13:08:23 UTC

Joined: Thu, 27 Oct 2011 12:56:03 UTC
Posts: 5
Can you tell me how to find if the following equation has a solution?

DA=b
where D is an 1 x m matrix with unknown elements,
A is an m x n matrix with known elements,
and b is an 1 x n matrix in which all elements are equal to 1.

Thank you,
Anna

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 Post subject: Re: how to find if this equation has a solution?Posted: Thu, 27 Oct 2011 13:13:37 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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anna wrote:
Can you tell me how to find if the following equation has a solution?

DA=b
where D is an 1 x m matrix with unknown elements,
A is an m x n matrix with known elements,
and b is an 1 x n matrix in which all elements are equal to 1.

Thank you,
Anna

This is equivalent to the assertion the row space of A contains (1,1,...,1).

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 Post subject: Re: how to find if this equation has a solution?Posted: Fri, 28 Oct 2011 12:22:03 UTC

Joined: Thu, 27 Oct 2011 12:56:03 UTC
Posts: 5
What does it mean 'the row space of A contains (1,1,...,1)'?

Is it right that, if A has rank m, this means that A*pseudoinverse(A) is equal to the m x m unity matrix?

Anna

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 Post subject: Re: how to find if this equation has a solution?Posted: Fri, 28 Oct 2011 13:29:58 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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anna wrote:
What does it mean 'the row space of A contains (1,1,...,1)'?

Is it right that, if A has rank m, this means that A*pseudoinverse(A) is equal to the m x m unity matrix?

Anna

Do you know what the row space is?

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 Post subject: Re: how to find if this equation has a solution?Posted: Sat, 29 Oct 2011 06:40:10 UTC

Joined: Thu, 27 Oct 2011 12:56:03 UTC
Posts: 5
I do not know what is the row space.

Maby there is a solution when there is a linear combination of the rows of A that is equal to an 1 x n matrix of ones.

http://en.wikipedia.org/wiki/Moore%E2%8 ... udoinverse

in paragraph 4.4. something about finding a right inverse that could help me to solve the problem. But I do not understand if this holds for every m x n matrix A that has rank equal to m.

Anna

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 Post subject: Re: how to find if this equation has a solution?Posted: Sat, 29 Oct 2011 07:34:54 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
anna wrote:
I do not know what is the row space.

Maby there is a solution when there is a linear combination of the rows of A that is equal to an 1 x n matrix of ones.

http://en.wikipedia.org/wiki/Moore%E2%8 ... udoinverse

in paragraph 4.4. something about finding a right inverse that could help me to solve the problem. But I do not understand if this holds for every m x n matrix A that has rank equal to m.

Anna

You should google "row space" instead, that's the crux of the matter.

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 Post subject: Re: how to find if this equation has a solution?Posted: Sun, 30 Oct 2011 06:15:55 UTC

Joined: Thu, 27 Oct 2011 12:56:03 UTC
Posts: 5
Ok, thank you. I read about the row space. So if I understand, the problem has a solution when there is a linear combination of the row vectors of A that is equal to (1, 1, ... ,1).

However there is something that I do not understand in the link I have sent in my previous post. If the rows of A are linearly independent this means that the pseudoinverse of A is a right inverse of A?

Anna

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