For the following three augmented matrices, would it be true to say that all of the the coefficient columns are linearly dependent, as the rank of the matrix in each case is less than the amount of coefficient columns?

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- Mar 27th 2009, 03:24 PMCrakaRank of matrix in determining linear dependence
For the following three augmented matrices, would it be true to say that all of the the coefficient columns are linearly dependent, as the rank of the matrix in each case is less than the amount of coefficient columns?

- Mar 27th 2009, 05:42 PMNonCommAlg
in general in any matrix with entries in a field, if then the columns of the matrix are linearly dependent. the reason is that the the dimension of the column space (rank) is at most

and we have vectors (columns) in that space. since those vectors cannot be linearly independent.