Solutions to Linear EquationsDate: 09/21/2001 at 05:27:22 From: Nanda Subject: Linear equations Dear Dr. Math, Can you specify the conditions under which a a system of linear equations has infinitely many solutions, a unique solution and no solution? Date: 09/21/2001 at 11:51:37 From: Doctor Rob Subject: Re: Linear equations Thanks for writing to Ask Dr. Math, Nanda. Let S be the field from which the coefficients and solution values are drawn. Let V be the number of variables, and E the number of *independent* equations. Then: 1. If E > V, the number of solutions is 0. 2. If E = V, the number of solutions is 1. 3. If E < V and S is finite, then the number of solutions is a power of the size of S. 4. If E < V and S is infinite, then the number of solutions is infinite. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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