EEL5173 Fall 2009 Lecture _20

# EEL5173 Fall 2009 Lecture _20 - iv Elementary Row(Column...

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Unformatted text preview: iv. Elementary Row (Column) Operations- to find a gcrd ( gcld .) (1) Interchange of rows (columns) 1 1 W W L = ) ( a a W WR = (2) Multiplication of a non-zero constant to a row (column) 2 2 W W L = ) ( b b W WR = Note: Multiplication of a non-constant polynomial to a row or a column is not an elementary operation. , ) ( 1 1 1 1 1 ) ( ) ( ) ( ) ( ) ( ) ( 43 42 41 33 32 31 23 22 21 13 12 11 43 42 41 33 32 31 23 22 21 13 12 11 q q R s q I s W w s q w w w s q w w w s q w w w s q w w w w w w w w w w w w w w s W = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⇒ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⋅ ⋅ ⋅ ⋅ ⇒ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = x q ( s ) q ( s ) = ( s 2 +1) not unimodular. x q ( s ) Ex. ) ( ) ( ) ( ) ( ) ( 3 43 42 41 33 32 31 23 22 21 23 13 22 12 21 11 43 42 41 33 32 31 23 22 21 13 12 11 s W w w w w w w w w w w s q w w s q w w s q w w w w w w w w w w w w w s W = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⋅ + ⋅ + ⋅ + ⇒ ⎥ ⎥...
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EEL5173 Fall 2009 Lecture _20 - iv Elementary Row(Column...

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