Example of REF and RREF.pdf

# Example of REF and RREF.pdf - University of Toronto at...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23S How to Reduce a Matrix to a REF A matrix A can be reduced to a row echelon form (REF) by using a series of elementary row operations: 1. Find the leftmost column that contains nonzero entries. Call this the ”pivotal working” column. 2. Choose one of the rows that have a nonzero entry in the ”pivotal work- ing column” (if possible, choose a row with 1 in that column). Inter- change this row with row one so as to have a nonzero entry in ”pivotal working column” of the first row. Now the first row is called the ”piv- otal working row”. 3. Call the first nonzero entry of the ”pivotal working row” a pivot of this row. If this pivot is not equal to 1, then multiply each element in the row by the reciprocal of the pivot, so as to have a pivot of 1. 4. Add multiples of the pivotal working row to each of the rows beneath it, so every entry in the ”pivotal working column” below the pivot will be 0.
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