notes1-2 - SECTION 1.2 ROW REDUCTION AND ECHELON FORMS Our...

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SECTION 1.2 ROW REDUCTION AND ECHELON FORMS Our aim is to transform a system of linear equations into an equivalent system from which the solutions can easily be read. It’s easiest to do this by performing row operations on the augmented matrix of the system in order to change the matrix into echelon form, and then into reduced echelon form. EXAMPLE. 2 0 4 3 6 1 0 0 5 1 2 2 0 0 0 1 2 3 0 0 0 0 4 4 0 0 0 0 0 0 TERMS: Nonzero row or column leading entry echelon form: all nonzero rows are at the top, leading entries go from upper left to lower right (so that entries below a leading entry are all zeros) reduced echelon form: in addition, leading entries are 1’s and have zeros above as well as below pivot position: location in a matrix that corresponds to a leading 1 in its reduced echelon form pivot column: a column in a matrix that contains a pivot position pivot: a nonzero number in a pivot position
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notes1-2 - SECTION 1.2 ROW REDUCTION AND ECHELON FORMS Our...

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