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Math Help - Vectors matrix problem

  1. #1
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    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)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by buckaroobill View Post
    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
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  3. #3
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    what is the definition of "linearly dependent?"
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  4. #4
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    Quote Originally Posted by buckaroobill View Post
    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
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  5. #5
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    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.
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