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simplifyingmatrices

simplifyingmatrices - non-zero entry in Row 3 etc • At...

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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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