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 132 222 357 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 21 100 210 001 E =− times A = To replace row 3 with row 3 - 3 row 1 use the matrix 31 010 301 E = times A = 31 21 EE = Times A =
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Then replace row 3 with the multiple of row 2 - 2. Multiplication of a Row by a nonzero real number. This matrix is the identity with the multiplication factor replacing the 1 on that row.
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This note was uploaded on 08/10/2011 for the course MATH 2331 taught by Professor Staff during the Spring '08 term at University of Houston.

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

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