row_echelon_solutions

row_echelon_solutions - Math 568 Row Echelon Form and...

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Math 568 Row Echelon Form and Number of Solutions 1. Row Echelon Form In these notes we will define one of the most important forms of a matrix. It is one of the “easier” forms of a system to solve, in particular, only back-substitution is needed to complete the solution of the corresponding linear system. Perhaps more importantly, this form allows us to determine the number of solutions that the corresponding linear system has. Recall that a linear system can either be inconsistent (have no solution) or be consistent. Furthermore, if the system is consistent it can either have a unique solutions or infinitely many solutions. There are no other possibilities. First we need some definitions: Definition 1.1. Let A be a coefficient or [ A | b ] an augmented matrix of some linear system. (1.) The leading entry in a row of A or [ A | b ] is the first non-zero entry (from left to right) in that row of A or [ A | b ] . (2.)
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This note was uploaded on 02/27/2012 for the course MATH 568 taught by Professor White during the Winter '08 term at Ohio State.

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row_echelon_solutions - Math 568 Row Echelon Form and...

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