simplifyingmatrices

simplifyingmatrices - non-zero entry in Row 3, etc. At the...

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Strategy for simplifying matrices: General strategy - • Obtain zeroes where required first. • After the required zeroes are obtained, divide each row by the necessary non- zero number to obtain a “1” as the first non-zero entry for each row. (Save this step until the last because it often involves the introduction of fractions.) More detailed strategy - • Use Row 1 to zero out the entries in Column 1 below the entry in Row 1 and Column 1 . (For instance, zero out the entry in Row 2 and Column 1 by replacing Row 2 with the sum of a multiple of Row 1 plus a multiple Row 2. Choose the multiples so that the resulting Row 2 has a zero as its first entry.) • Continue this process until the matrix has zeroes below the first non-zero entry in each row. That is, use Row 2 to zero out the entries below the first non-zero entry in Row 2; use Row 3 to zero out the entries below the first
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Unformatted text preview: non-zero entry in Row 3, etc. At the last step, multiply each row with a non-zero entry by the reciprocal of its first non-zero entry. Additionally - At each step in the process, check to see if all the entries in any row have a nontrivial common multiple. If so, divide the row by that common multiple. (This will keep the magnitude of the calculations minimal.) If any row contains all zeros, move that row to the bottom of the matrix. Variation on the process - The matrix resulting from the above simplification will be in echelon form . To obtain a matrix in reduced row echelon form , use Row 2 to zero out the entries above and below the first non-zero entry in Row 2. Similarly, if necessary, use Row 3 to zero out the entries above the first non-zero entry in Row 3....
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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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