# confused.

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• Nov 14th 2009, 06:16 AM
alexandrabel90
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?
• Nov 14th 2009, 06:29 AM
HallsofIvy
Quote:

Originally Posted by alexandrabel90
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.