Say we are given a matrix:

A =

(1 3)

(1 0)

(2 1)

How do we find the set of vectors that are in the row space of A?

Do we do this by row reducing the following matrix?

(1 3 | 0)

(1 0 | 0)

(2 1 | 0)

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- March 9th 2007, 06:16 PMbuckaroobillVectors matrix problem
Say we are given a matrix:

A =

(1 3)

(1 0)

(2 1)

How do we find the set of vectors that are in the row space of A?

Do we do this by row reducing the following matrix?

(1 3 | 0)

(1 0 | 0)

(2 1 | 0) - March 9th 2007, 10:57 PMCaptainBlack
The row space of a matrix is the space spanned by its rows. If this matrix has two linearly dependent rows (and it does) then as the rows are 2-vectors the row space is either R^2 or C^2 depending on if we are dealing with real or complex spaces/matrices.

RonL - March 10th 2007, 03:39 PMbuckaroobill
what is the definition of "linearly dependent?"

- March 10th 2007, 03:44 PMThePerfectHacker
How can you ask a question like that?

You are in a Linear Algebra class, already done that, it is fundamental to know and still not know it. Further you have a textbook which gives the definitions!

Here - March 10th 2007, 04:25 PMPlato
I don’t think that this in a traditional “Linear Algebra” class.

There are “classical matrices” classes.

In these ‘linear independence’ is not a topic.