100224_Matrices_Outline

100224_Matrices_Outline - operation on In The elementary...

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Let A be an m × n matrix. Any one of the following three operations on the rows [columns] of A is called an elementary row [column] operation: 1 interchanging any two rows [columns] of A. (type 1) 2 multiplying any row [column] of A by a nonzero scalar.(type 2) 3 adding any scalar multiple of a row [column] of A to another row [column].(type 3) L n n × n elementary matrix is a matrix obtained by performing an elementary
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Unformatted text preview: operation on In. The elementary matrix is said to be of type 1, 2, or 3 according to whether the elementary operation performed on In is a type 1, 2, or 3 operation, respectively. Elementary matrices are invertible, and the inverse of an elementary matrix is an elementary matrix of the same type....
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