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Math Help - confused.

  1. #1
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    confused.

    hi

    as long as i can show that the column vectors of A ( 3 X 4 matrix ) is linearly dependent, which is easy since the no. of columns is more than that of rows, it shows that B being expressed as a linear combination of
    A is not unique for Ap = B right?

    in this case, im also saying that if the no. of columns is more than the no of rows in the column vectors of A, then the column vectors in A are linearly dependent...

    am i right to say that?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    hi

    as long as i can show that the column vectors of A ( 3 X 4 matrix ) is linearly dependent, which is easy since the no. of columns is more than that of rows, it shows that B being expressed as a linear combination of
    A is not unique for Ap = B right?

    in this case, im also saying that if the no. of columns is more than the no of rows in the column vectors of A, then the column vectors in A are linearly dependent...

    am i right to say that?
    Yes. If the number of rows is n and the number of columns is m, m> n, then the "column vectors" are vectors in R^n and it is impossible to have a set of m independent vectors in a space of dimension less than m.
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