Elementary Row Operations
Elementary Row Operations
Elementary row operations:
Replace: replace one row by the sum of that row and a constant multiple of another row.
Swap: interchange two rows
Scale: multiply a row by a non-zero constant
Let's use the elementary row operations to reduce a matrix to row echelon form.
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Elementary Matrices
Define procedures which create elementary matrices.
Premultiplication of a given matrix by an elementary matrix effects an elementary row operation.
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Testing. Create some elementary matrices.
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Echelon Form
Use elementary row operations to reduce a matrix to row echelon form.
Premultiplication by elementary matrices accomplishes the transformation.
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Reduced Echelon Form
Use row reduction to solve a system of linear equations.
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Let's check that.
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Created by Mathematica (December 15, 2004) | ![]() |