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2331_Notes_2o6_fill

# 2331_Notes_2o6_fill - Math 2331 Linear Algebra Section 2.6...

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Math 2331 Linear Algebra Section 2.6 Elimination and Factoization A=LU Elimination - Goal: Reduce a matrix A to an upper triangular matrix U so that Ax=b may be solved by back substitution with U. The process of elimination may be represented as multiplication by invertible elimination matrices (from the left). Let's first look at these matrices Legal Elimination Operations Let's work with the matrix 1 3 2 2 2 2 3 5 7 A = 1. Replace Row i by Row i minus a multiple c of row j. This matrix is and this is the identity matrix plus the number -c in the i,j position ij E To replace row 2 with row 2 - 2 row 1 use the matrix 21 1 0 0 2 1 0 0 0 1 E = times A = To replace row 3 with row 3 - 3 row 1 use the matrix 31 1 0 0 0 1 0 3 0 1 E = times A = 31 21 E E = Times A =

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