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**virtualinsanity****Member**- Registered: 2007-03-11
- Posts: 38

There's this problem in my linear algebra book:

Describe the vectors which are in the row space of the following matrix:

(1 3

2 0

-1 1)

I was wondering how this is done so if anyone could help, that would be great! Thanks!

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

I'm never sure what math people mean when they say "describe". I think they probably mean that they want you to find out if they are linearly dependent or not.

El que pega primero pega dos veces.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

When youve found a basis for the space, you will have described the vectors in the space (since every vector is a linear combination of the basis vectors).

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**virtualinsanity****Member**- Registered: 2007-03-11
- Posts: 38

JaneFairfax wrote:

When youve found a basis for the space, you will have described the vectors in the space (since every vector is a linear combination of the basis vectors).

Does this mean that I have to put this matrix in row-reduced echelon form? As in row reduce the following...

(1 3| 0)

(2 0| 0)

(-1 1| 0)

?

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,379

ie

a(1 3)+b(2 0) represents any vector composed by row vectors of the Matrix.

**X'(y-Xβ)=0**

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**virtualinsanity****Member**- Registered: 2007-03-11
- Posts: 38

Oh, okay. So I put the matrix in row-reduced echelon form and got the matrix:

1 0 | 0

0 1 | 0

0 0 | 0

Does this mean that the set of vectors in the row space of a are just (0,0) since:

a = 0

b = 0

Therefore, 0(1 3) + 0(2 0) = (0 0) if I'm not mistaken?

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,379

No, row space means any another vector with the same amount of entries can be represented by a linear combination of the given row vectors from the matrix.

**X'(y-Xβ)=0**

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