Unformatted text preview: 2 – by– 2 submatrix in the i –th and j –th rows and i –th and j –th columns, which is equal to ± ˛ ˇ ± ı ² . For example, when m D 4 , U. ± ˛ ˇ ± ı ² I 2;4/ D 2 6 6 4 1 0 0 0 0 ˛ 0 ˇ 0 0 1 0 0 ± 0 ı 3 7 7 5 : The matrix U. ± ˛ ˇ ± ı ² I i;j/ is invertible with inverse U. ± ˛ ˇ ± ı ² ± 1 I i;j/ . Left multiplication by U. ± ˛ ˇ ± ı ² I i;j/ implements the fourth type of elementary row operation. Elementary column operations are analogous to elementary row operations. They are implemented by right multiplication by invertible n –by– n matrices. We say that two matrices are row–equivalent if one is transformed into the other by a sequence of elementary row operations; likewise, two matrices are column–equivalent if one is transformed into the other by a...
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 Fall '08
 EVERAGE
 Linear Algebra, Algebra, Invertible matrix, row operation

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