Thread: Vectors 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)

Originally Posted by buckaroobill

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)

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

what is the definition of "linearly dependent?"

Originally Posted by buckaroobill

what is the definition of "linearly dependent?"

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

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.