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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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row_echelon_solutions - Math 568 Row Echelon Form and...

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