echelon

echelon - A matrix is in echelon form when: 1) Each row...

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A matrix is in echelon form when: 1) Each row containing a non-zero number has the number “1” appearing in the row s first non-zero column. (Such an entry will be referred to as a “leading one”.) 2) The column numbers of the columns containing the first non-zero entries in each of the rows strictly increases from the first row to the last row. (Each leading one is to the right of any leading one above it.) 3) Any row which contains all zeros is below the rows which contain a non-zero entry. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The three conditions above will ensure that the entries below the leading ones (in each row which contains a non- zero entry) are all zeros . ______________________________________________ A matrix is in reduced echelon form when: in addition to the three conditions for a matrix to be in echelon form, the entries above the leading ones (in each row which contains a non-zero entry)
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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echelon - A matrix is in echelon form when: 1) Each row...

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