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Systems of Linear Equations

Part 7: Module Summary

  1. When we try to solve a system of m linear equations in n unknowns, there are only three possible outcomes for the number of solutions. What are those possibilities?

  2. If the system has 2 unknowns, then it can be described in terms what geometric objects? What are the possible configurations of these objects? Which configurations represent consistent systems? Which represent inconsistent systems?

  3. If the system has 3 unknowns, then it can be described in terms what geometric objects? What are the possible configurations of these objects? Which configurations represent consistent systems? Which represent inconsistent systems?

  4. If the system is consistent, then there is a relationship between the number of free variables in the solution, the number of nonzero rows in the reduced row echelon form of the augmented matrix, and the number of unknowns. What is that relationship?
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