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In the preceding chapter we described the form taken by the solution of an m × n system of equations. The form of this solution depended essentially on the rank of the system, that is the maximum number of linearly independent columns; but since the process of solving the equations also provided the value of the rank, we did not need any special methods for determining the rank. In fact almost every method for determining the rank of a system is similar (and comparable in length) to the method of solving the equations given in chapters II and IV. Nevertheless it is often useful to have another characterization of the rank, and in particular, to have a criterion for the hnear dependence of n vectors in n dimensions.
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