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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 . For example, when m D 4 , U. I 2;4/ D 2 6 6 4 1 0 0 0 0 0 0 0 1 0 0 0 3 7 7 5 : The matrix U. I i;j/ is invertible with inverse U. 1 I i;j/ . Left multiplication by U. I i;j/ implements the fourth type of ele-mentary row operation. Elementary column operations are analogous to elementary row oper-ations. They are implemented by right multiplication by invertible n by n matrices. We say that two matrices are rowequivalent if one is transformed into the other by a sequence of elementary row operations; likewise, two matrices are columnequivalent if one is transformed into the other by a...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08