solved08 - S 8.1 _ A square matrix is tested for...

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S 8.1 ______ A square matrix is tested for singularity in the forward phase of Gaussian elimination. If a zero element is encountered on the leading diagonal, then row interchanges are used to replace that element by a nonzero value (from another UNUSED row). The matrix is singular if and only if: a zero element on the leading diagonal cannot be removed by row interchanges - i.e., all remaining (unused) rows have zeros in the same column. Row interchanges can be shown explicitly (by swapping rows on the table), or indicated by marking (circle, underline, asterisk, etc.) the pivot element at each stage. We use the latter approach, where the column 'p' keeps track of the USED rows. Matrix A ________ p m x1 x2 x3 x4 ____________________________________________ * 3* 1 -2 5 3 -9 -4 5 -11 4 -12 -3 9 -24 -1 3 0 5 6 ____________________________________________ * 3 1 -2 5 * 0 -1* -1 4 1 0 1 1 -4 -1 0 -1 7 1 ____________________________________________ * 3 1 -2 5 * 0 -1 -1 4 0 0 0 0 * 0 0 8* -3 ____________________________________________ The only possible pivot for x3 is in the fourth row (=8, marked).
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This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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solved08 - S 8.1 _ A square matrix is tested for...

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